EMH are busy days full stop. We avoid them. The nights when we have hit Magic Kingdom and it is an evening EMH the lines are the longest we have ever seen, and the crowd levels are bursting out. We only go in for the fireworks but it does make me wonder why it is considered a perk when the lines are longer than normal.
The morning ones are not that much of a problem, however, though the park will be busier as a whole, because we get to the park for opening times anyway. Fortunately, people like to lie in so I don't believe EMH mornings are as busy as late evening ones. If we have hit a park with EMH morning we have still managed to get around the rides quickly but not the same as a non EMH day.