You could, but I bet you'd be nearly (or fully) complete with breakfast and even if you signed up quickly, your party would be waiting on you back at the restaurant. I think you'd be best off trying to get and settle your check mid way through the meal and be prepared for the Jedi folks to just leave while the rest of your party finishes at their leisure.
ETA: I've eaten at H&V and done jedi sign-ups, but not the early ADR straight to Jedi, so if others have a more direct experience, go with that!