I was there last May and I ordered kids meals for myself at most of the counter service places with no problems. I ordered them because of the less expensive price, what was included (healthy side like grapes and a milk or bottled water), and the portion size was more what I wanted. I didn't want to pay for a huge thing only to eat a 1/4 of it. I look young but at 5'10, can't really pass for a kid. Nor was I asked to show one to get the meal. I considered it similar to McDonalds and the Happy Meals. They don't ask for proof there either.
I can't answer about Table service. I jwould just think if you're doing it they care less at CS where there's no tips or any kind of money they're losing out on. Whether you order a kids or adult meal, its the same to the cast member. In a TS, not so much.