When we have been for early EMH, they have always done the show. To be safe, we always arrive at least 30 minutes before the park is scheduled to open. I don't have the exact start time, but I would guess it starts 15 minutes before park opening?
So if EMH start at 8:00am, I would get there at 7:30 at the latest. We always aim for 7 or 7:15 and bring our breakfast with us!