If you're just getting an entree, you may have a shot. But if you're on a plan that gives you appetizer, entree, and dessert, I think I'd plan to ask for app and entree at the same time, then ask for the bill the moment that dessert is delivered. It will definitely be tight.
Like Pakey, I've had first seating several times, and I don't think I've been out in an hour either. And that was without a dining plan, i.e. single course meals. At least once it took 10-15 minutes just to get seated, and that was despite arriving early.