We had our 6 week old there (also our almost 2, and almost 3 year old too). The baby was the easiest! She slept, and spent ALL day in the sling, she was great. When she was awake she loved the music and the lights, almost all of the characters googled over her.
I think it all depends on how easy the baby is, and how the parents are. We are very laid back, not germaphobs at all, so we were not worried about it at all. But, I have a friend who did not allow visitors, or to leave the house (except for doctor visits) for 12 weeks after the baby is born.
We had our girls knowing we were going to have to slow life down to there pace, but that has not prevented us from traveling, or enjoying all the other things we used to do.
No, none of my girls remember there first trip to disney, but they also don't remember the days there were born, the first day they crawled, there first birthdays, first playdates, and a lot of other things. They still enjoyed it as much as they did this year at 2, 4, and 5.
We also travel light, we (even the first trip, with a newborn) only brought one stoller, my kids have ALL hated the stoller...preferred to walk (actually the oldest runs everywhere...always) most of the time. The baby was always in the sling so it was easy for us. I would do it again with a newborn anyday over a new crawler (8, 9, 10 month old) That would of been harder for me.
I am sure you will get all sorts of responses, but for us it was magical in every way with a tiny one.