It depends on the restaurant so it would help if you tell us which restaurants you are asking about.
Some TS restaurants remain open during the party, but others do not. For the TS restaurant, if you go to its regular reservation page it will show the hours for dinner and the drop down bar will show the last dining reservation time that can be booked without party tickets. For TS restaurants that are open during the party you have to book specifically through the party dining reservation page which will show the reservation times that require party tickets and will mention more than once that party tickets are required to dine.
The larger QS restaurants usually have their hours listed on the weekly Times Guide. For Quick Service, once it is for ticketed party goers only, there is usually a castmember at the door checking for wristbands. Some QS close early on party days because they are used as treat venues during the party and need time to prepare.