Our honeymoon coincided with Gay Days in 2001. I didn't realize this until after we'd booked, so we were quite worried about crowds as well. However, we didn't notice any real difference in crowds than in other times we've gone in late May. We went to Epcot on 'the' Saturday, and didn't really find it crowded there at all (for that time of the year that is). We heard from other people in Epcot, though, that the MK was indeed very, very crowded.
The following week, it was perhaps slightly less crowded but I don't think there was any big change in wait times or crowds.
We did get a letter under the door earlier in the week that said all the parks would open at 7:30 a.m. that day, only for resort guests since they were "expecting a very busy day at the Magic Kingdom Park."
Behaviour-wise, well, I can't comment on MK because we didn't go over there for the 'main event', but at Epcot and the other parks during the week, I can't remember seeing anything that we haven't seen at WDW at other times of the year.