We have done this one time with no problem. Our kids are on the pickier side and we have always found something on the menu they will eat at table service restaurants. I guess it will depend on the restaurant.
DS7 & DS5 are pretty picky as well, and we've not had a problem finding something for them to eat at TS restaurants. It seems there's always at least one of the following on the kids' menu no matter where you go: pizza, spaghetti, mac n cheese, chicken fingers, pb & j. And if there's not, I'll bet you could ask and they'd find something for you. And, if you do the buffets, it's hard not to find things they'll eat. CP is a favorite of ours for that reason.