You may get more response to this on the Theme Parks Board.
I think that there is a series of "levels" that the parks go through when they reach capacity numbers. IIRC it starts will closing to Off Site Guests but On Site Guests are still let in and then goes to absolutely no one being allowed in.
But there is no way to really predict what the crowd level will be at the different times of day. If they have reached a capacity where they have to close to everyone, even if it is EMH then you won't be able to get in. I have no idea how likely that is though.