At the end of the day they are no different to the catholics, only that the catholics were in the past an oppressive religion and the jws are so in the present, so I don't think they would mind having that library card.
They probably have one under an assumed name. I bet the Vatican throws them out if they ever find out the WTS has one because of all the nice compliments their literature has been bestowing on the Catholics for the last 125 years.
I would love to see the Vatican Library, think of all those manuscripts! There's also a lot of forgeries there too, but it would be interesting to wade through it all.
As for the WT using that library, since they have no academics with degrees (usually need a doctorate to gain access) they wouldn't be able to enter anyway.
objection: Witness apologist Greg Stafford offers a number of arguments in favor of the NWT punctuation of Luke 23:43.
Codex Vaticanus
His first is that a major early manuscript of the New Testatment contains a punctuation mark - equivalent to a comma - after "today," just as does the NWT:
While punctuation in NT manuscripts of the first few centuries CE is not common, one of the best, if not the best witness to the text of the NT, Codex B or Vaticanus (Vatican 1209) of the fourth century CE, does have a mark of punctuation in Luke 23:43; the punctuation is not after “I say” but after the Greek word sêmeron, “today" (Stafford, pp. 546-547).