As a JW, I would answer "No", or what sir82 said, "Jehovah is the judge."
As a non-JW, I would answer "yes" for these reasons:
First, everyone is ELIGIBLE for the benefits of Christ's ransom. Everyone. It's up to each person as to whether they will do what Christ says to do or not.
That said, Paul refused to preach the way JWs preach. Romans 15:20,21: " In this way, indeed, I made it my aim not to declare the good news where the name of Christ had already been made known, so as not to build on another man’s foundation; but just as it is written: “Those who received no report about him will see, and those who have not heard will understand."" So, this man in your hypothetical situation, should not even be approached by JWs since he is ALREADY a believer. So, JWs, in preaching where Christ has already been named, run the risk of subverting peoples' faith.
Christ gave the command to "Go and make disciples." Of whom? Based on the context, of himself. JWs do NOT make disciples of Christ. That isn't their aim. They view themselves as rescuers. In one of this year's Circuit Assembly programs, they drive this point in and state it's their commission, based on Proverbs 24:11: "Rescue those who are being taken away to death, And hold back those staggering to the slaughter." So, JWs preaching some other doctrine could actually make THEM ineligible. Why? Because while they are preaching, they are not doing what Christ commanded, to make disciples of him and teach people to observe ALL HIS commandments. This, in my opinion, is disobedience. They are going beyond what Christ said to do, and, in fact, actually NOT doing what he DID say to do.
As for "spirit and truth", it's hard to worship with "truth" if truth is constantly changing.