For complicated reasons that I'm not going to go into right now, the JWs view it as very important that Judas left BEFORE the bread and wine was passed around.
But did he?
According to Matthew:
(Matthew26:19-36) . . .and they got things ready for the passover. 20 When, now, it had become evening, he was reclining at the table with the twelve disciples. 21 While they were eating, he said: "Truly I say to YOU, One of YOU will betray me." 22 Being very much grieved at this, they commenced each and every one to say to him: "Lord, it is not I, is it?" 23 In reply he said: "He that dips his hand with me in the bowl is the one that will betray me. 24 True, the Son of man is going away, just as it is written concerning him, but woe to that man through whom the Son of man is betrayed! It would have been finer for him if that man had not been born." 25 By way of reply Judas, who was about to betray him, said: "It is not I, is it, Rabbi?" He said to him: "You yourself said [it]." 26 As they continued eating, Jesus took a loaf and, after saying a blessing, he broke it and, giving it to the disciples, he said: "TAKE, eat. This means my body." 27 Also, he took a cup and, having given thanks, he gave it to them, saying: "Drink out of it, all of YOU; 28 for this means my ‘blood of the covenant,’ which is to be poured out in behalf of many for forgiveness of sins. 29 But I tell YOU, I will by no means drink henceforth any of this product of the vine until that day when I drink it new with YOU in the kingdom of my Father." 30 Finally, after singing praises, they went out to the Mount of Olives. 31 Then Jesus said to them: "All of YOU will be stumbled in connection with me on this night, for it is written, ‘I will strike the shepherd, and the sheep of the flock will be scattered about.’ 32 But after I have been raised up, I will go ahead of YOU into Gal´i·lee." 33 But Peter, in answer, said to him: "Although all the others are stumbled in connection with you, never will I be stumbled!" 34 Jesus said to him: "Truly I say to you, On this night, before a cock crows, you will disown me three times." 35 Peter said to him: "Even if I should have to die with you, I will by no means disown you." All the other disciples also said the same thing. 36 Then Jesus came with them to the spot called Geth·sem´a·ne. . .
Matthew doesn't mention Judas leaving at all.
According to Mark:
(Mark 14:16-26) . . .and they prepared for the passover. 17 After evening had fallen he came with the twelve. 18 And as they were reclining at the table and eating, Jesus said: "Truly I say to YOU, One of YOU, who is eating with me, will betray me." 19 They started to be grieved and to say to him one by one: "It is not I, is it?" 20 He said to them: "It is one of the twelve, who is dipping with me into the common bowl. 21 True, the Son of man is going away, just as it is written concerning him, but woe to that man through whom the Son of man is betrayed! It would have been finer for that man if he had not been born." 22 And as they continued eating, he took a loaf, said a blessing, broke it and gave it to them, and said: "Take it, this means my body." 23 And taking a cup, he offered thanks and gave it to them, and they all drank out of it. 24 And he said to them: "This means my ‘blood of the covenant,’ which is to be poured out in behalf of many. 25 Truly I say to YOU, I shall by no means drink anymore of the product of the vine until that day when I drink it new in the kingdom of God." 26 Finally, after singing praises, they went out to the Mount of Olives.
Mark doesn't mention Judas leaving either.
According to Luke:
(Luke22:13-39) . . .and they got the passover ready. 14 At length when the hour came, he reclined at the table, and the apostles with him. 15 And he said to them: "I have greatly desired to eat this passover with YOU before I suffer; 16 for I tell YOU, I will not eat it again until it becomes fulfilled in the kingdom of God." 17 And, accepting a cup, he gave thanks and said: "Take this and pass it from one to the other among yourselves; 18 for I tell YOU, From now on I will not drink again from the product of the vine until the kingdom of God arrives." 19 Also, he took a loaf, gave thanks, broke it, and gave it to them, saying: "This means my body which is to be given in YOUR behalf. Keep doing this in remembrance of me." 20 Also, the cup in the same way after they had the evening meal, he saying: "This cup means the new covenant by virtue of my blood, which is to be poured out in YOUR behalf. 21 "But, look! the hand of my betrayer is with me at the table. 22 Because the Son of man is going his way according to what is marked out; all the same, woe to that man through whom he is betrayed!" 23 So they started to discuss among themselves the question of which of them would really be the one that was about to do this. 24 However, there also arose a heated dispute among them over which one of them seemed to be greatest. 25 But he said to them: "The kings of the nations lord it over them, and those having authority over them are called Benefactors. 26 YOU, though, are not to be that way. But let him that is the greatest among YOU become as the youngest, and the one acting as chief as the one ministering. 27 For which one is greater, the one reclining at the table or the one ministering? Is it not the one reclining at the table? But I am in YOUR midst as the one ministering. 28 "However, YOU are the ones that have stuck with me in my trials; 29 and I make a covenant with YOU, just as my Father has made a covenant with me, for a kingdom, 30 that YOU may eat and drink at my table in my kingdom, and sit on thrones to judge the twelve tribes of Israel. 31 "Simon, Simon, look! Satan has demanded to have YOU men to sift YOU as wheat. 32 But I have made supplication for you that your faith may not give out; and you, when once you have returned, strengthen your brothers." 33 Then he said to him: "Lord, I am ready to go with you both into prison and into death." 34 But he said: "I tell you, Peter, A cock will not crow today until you have three times denied knowing me." 35 He also said to them: "When I sent YOU forth without purse and food pouch and sandals, YOU did not want for anything, did YOU?" They said: "No!" 36 Then he said to them: "But now let the one that has a purse take it up, likewise also a food pouch; and let the one having no sword sell his outer garment and buy one. 37 For I tell YOU that this which is written must be accomplished in me, namely, ‘And he was reckoned with lawless ones.’ For that which concerns me is having an accomplishment." 38 Then they said: "Lord, look! here are two swords." He said to them: "It is enough." 39 On going out he went as customarily to the Mount of Olives. . .
According to Luke Jesus said that the betrayer was AT THE TABLE, right after they passed the wine and bread. So according to Luke, Judas was present during the passing of the emblems. Luke does not mention Judas leaving.
According to John:
(John13:12-38)12 When, now, he had washed their feet and had put his outer garments on and laid himself down at the table again, he said to them: "Do YOU know what I have done to YOU? 13 YOU address me, ‘Teacher,’ and, ‘Lord,’ and YOU speak rightly, for I am such. 14 Therefore, if I, although Lord and Teacher, washed YOUR feet, YOU also ought to wash the feet of one another. 15 For I set the pattern for YOU, that, just as I did to YOU, YOU should do also. 16 Most truly I say to YOU, A slave is not greater than his master, nor is one that is sent forth greater than the one that sent him. 17 If YOU know these things, happy YOU are if YOU do them. 18 I am not talking about all of YOU; I know the ones I have chosen. But it is in order that the Scripture might be fulfilled, ‘He that used to feed on my bread has lifted up his heel against me.’ 19 From this moment on I am telling YOU before it occurs, in order that when it does occur YOU may believe that I am [he]. 20 Most truly I say to YOU, He that receives anyone I send receives me [also]. In turn he that receives me, receives [also] him that sent me." 21 After saying these things, Jesus became troubled in spirit, and he bore witness and said: "Most truly I say to YOU, One of YOU will betray me." 22 The disciples began to look at one another, being at a loss as to which one he was saying [it] about. 23 There was reclining in front of Jesus’ bosom one of his disciples, and Jesus loved him. 24 Therefore Simon Peter nodded to this one and said to him: "Tell who it is about whom he is saying [it]." 25 So the latter leaned back upon the breast of Jesus and said to him: "Lord, who is it?" 26 Therefore Jesus answered: "It is that one to whom I shall give the morsel that I dip." And so, having dipped the morsel, he took and gave it to Judas, the son of Simon Is·car´i·ot. 27 And after the morsel then Satan entered into the latter. Jesus, therefore, said to him: "What you are doing get done more quickly." 28 However, none of those reclining at the table knew for what purpose he said this to him. 29 Some, in fact, were imagining, since Judas was holding the money box, that Jesus was telling him: "Buy what things we need for the festival," or that he should give something to the poor. 30 Therefore, after he received the morsel, he went out immediately. And it was night. 31 Hence when he had gone out, Jesus said: "Now the Son of man is glorified, and God is glorified in connection with him. 32 And God will himself glorify him, and he will glorify him immediately. 33 Little children, I am with YOU a little longer. YOU will look for me; and just as I said to the Jews, ‘Where I go YOU cannot come,’ I say also to YOU at present. 34 I am giving YOU a new commandment, that YOU love one another; just as I have loved YOU, that YOU also love one another. 35 By this all will know that YOU are my disciples, if YOU have love among yourselves." 36 Simon Peter said to him: "Lord, where are you going?" Jesus answered: "Where I am going you cannot follow me now, but you will follow afterwards." 37 Peter said to him: "Lord, why is it I cannot follow you at present? I will surrender my soul in your behalf." 38 Jesus answered: "Will you surrender your soul in my behalf? Most truly I say to you, A cock will by no means crow until you have disowned me three times."
John stretches this scene out a lot more, it's several chapters, so I only quoted the important bits. John is the only one that mentions Judas leaving. But he does NOT mention the passing of the emblems.
So in conclusion:
Mathew records the passing of the emblems, but does not record Judas leaving beforehand.
Mark records the passing of the emblems, but does not record Judas leaving beforehand.
Luke records the passing of the emblems, and specifically says that Judas was present immediately afterward.
John does not record the passing of the emblems at all, but says that Judas left at some unknown time during the evening.