We were there that exact week last year (5/1) and I believe 5/5 was the "kick-off" for the "Happiest Celebration on Earth". There were a bunch of press events all week, some which closed each park early for the day, but it really didn't bother us.
Crowds were minimal at all the parks all week, even with some of them closing earlier. ADRs were easy to get too. I'm trying to plan a trip for that time this year as well. Weather was also good, not too hot, not too cold and not rainy at all.
The only grad events I knew of were the ones over the weekend which were at MK after regular hours. Didn't really notice anything out of the norm.