Yes, they do have pizzas.
One of the best things about Gasparilla's -- they are open 24 hours a day! After about 11pm the selection of hot foods is a bit limited, but you can order pizza, and there are pre-made salads, sandwiches, etc. in the cold cases, and plenty of snacks, beverages, ice cream available.
One of my favorite nights from my past GF trip was taking a midnight swim with my brother, followed by a trip to Gaspie's for ice cream and Guitar Hero at 2am.
One thing to note: it technically isn't a food court, it is a counter service restaurant. There are plenty of options to pick from, but it is definitely different than the true food courts you will find at the mods and deluxes.