B&C is a Table Service credit on the dining plan. The carry out window is not on the dining plan. They do not accept ADRs. The Kitchen Sink dessert is not part of the dining plan.
My thoughts....we love this restaurant, but I don't feel it is a good value to use it as a TS on the dining plan. If you need TS for something else, this is a good place to pay OOP. Alternatively, get your burgers at a CS place--the desserts won't be as good, but you can always choose to pay OOP for a sundae if you want one!