It may be an issue in some neighborhoods. We do not dine late here, and a lot of restaurant kitchens close at 11 pm. If you stay downtown (near the old city, either near the port or uptown around the walls) or in Sainte-Foy (what may be called somehow the financial district), you will be able to eat at 10 pm in most restaurants. But you may experience some quizzical looks (just so you know) if you want more than an appetizer of coffee and dessert.
Have a nice stay!