There is no proof, or even strong evidence, to support the claim that the WTS is the "faithful and discreet slave". Other posters have shown how the Society's own words and teachings can be used to prove the opposite, that the organization is not the slave. I want to add one more argument to support this.
If Jesus made his inspection and appointed a faithful slave in 1919, what would he have seen with respect to the WTS and its worthiness for this office? Well, in 1919, the Society was still teaching that the appointment had already been made and that Charles T. Russell was that faithful and discreet slave. Russell was dead by that time, but that was the official teaching. So if Jesus made any such appointment, the WTS would not have accepted it since it believed the office was already filled! It was not until 1927 that J.F. Rutherford decided that Russell was not the faithful and discreet slave and that the 'anointed remnant' was, but their own chonology shows that realization came too late, and the Lord would have chosen someone else.
You won't read any such admission in the literature, of course. Nor will you read, as other posters have pointed out, that since the WTS believed that Jesus had returned in 1874 and that Armageddon was scheduled to take place by October 1914 (later pushed ahead to 1915), that there could be no way the organization could be said to be serving 'meat in due season' as they put it. If the WTS was not serving the right spiritual food in 1919, then there is no way that it would have received Jesus' approval or appointment.
The Society might argue, "Ah, but that was back then and we have made all kinds of adjustments to our understanding showing that God was guiding us with his holy spirit and Jesus would have been pleased to appoint us as his 'faithful and discreet slave'." Well, even if that is true--which it most definitely isn't--it would still make no difference. Because what would matter is what the organization was teaching in 1919, not what it taught later or is teaching now. On that basis, there is no way the WTS would have received the coveted appointment.