It didn't affect the crowds in the day while we were there, and actually I think that some people left towards the end of the day.
When we did it MK was still full but most of those people didnt have wristbands. We walked right on space mountain and buzzlightyear. We didnt stay very late that night and went on only a couple rides.
I see that your going in May and we went in December, the crowds will surely be larger then.We did it for every park that had it on our trip. Morning is also good, we went to AK. They don't really have that much for morning hours, only the safari and it's tough to be a bug.
However we were able to ride primeval whirl and dinosaur right at 9 when everyone was still getting in the park. And we rode primeval whirl a few times in a row with very little wait.
I hear that EMH evening is busy and some people say not to even go because the crowds are so bad, but I've only had good experiences with it.