Very enjoyable discussion, thank you all!
To answer the somewhat more critical posts, yes, the time machine would allow the Time Traveller to visit all those times and places. The scenario simply extends however -- each thing you witness doesn't jibe with the NT, or is -- how to say it? -- a lesser version. I don't think it necessary to pick apart each and every event in the bible, but there would be some that -- if witnessed -- would be compelling, and others less so. Jesus is a pretty clever bloke when dealing with the Pharisees and Sanhedrin (until the end), but there's nothing particularly miraculous about him exposing them for the hypocrites they were.
OTOH, if he were to raise the dead (the daughter, Lazarus, himself) there'd be compelling evidence in favor of his godhood.
I especially like the question about belief versus humbling. While I do not believe in gods and such, I do not believe in them because for me the overall model is intrinsically flawed, undemonstrated, and I see no compelling evidence (and a discussion regarding this, if there's one to be had, belongs in another thread). I do not disbelieve because I am, like Satan is described, arrogant, prideful, hateful and challenging, etc. I simply find the proposal to be lacking in supportive merit.
However, even though I've come to this as a conclusion, I am -- as a rationalist -- a servant to compelling evidence. If I were given reasonable cause to believe in it, I would, and I would belive in it with all the attendant devotion required. I have a lot of problems with the anthropomorphic SuperMan gods of the bible, but if reality dictates they are in existence, then I have no choice but to acknowledge them and adhere to their desires.
So yes, I would both believe and humble myself.