It depends on the meal and the age of the kids. We have been to many character meals (1900 Park Faire, Castle Breakfast, Chef Mickeys, Crystal Palace, etc) and for the most part it has been too hectic for the kids to eat. Even when they were "supposed" to eat while waiting for their turn to meet the characters they spent more time looking around the room "spotting" them. It was a bit better at the buffet type meals because then they were at least up and about and "distracted" for a bit by choosing their food.
We went to Chef Mickey's for breakfast on our most recent trip and it was wonderful! We got there and went straight to the buffet (we were told it would be 20 minutes or so until the characters started coming to our table). My children ate so much! Then the characters came one after the other and it was perfect. But this was the first time a character meal went smoothly for us both in terms of food and character greetings.