No, character breakfasts have an additional cost. They're quite good fun and a nice way to start the day, as long as everyone eats, in our case we're always so desperate to get to the parks that it's a bit of a waste of money, as nobody eats much.
I can't remember how much extra it is offhand but it takes place at Cafe Mickey a restaurant in the village and there is a wider variety of food including sausages, bacon, pastries etc.
GMF's give you the oppportunity to have breakfast at the parks at no extra cost, so if you want to take advantage of Extra Magic Hours, but don't want a 7.00 breakfast at the hotel, you could opt for a later one in the park.
BTW If they're on, they're allocated on a first come first served basis, so ask when you check in what the availability is for your whole stay and hopefully you'll get 1 or 2.