Yes, you can use a pizza oven on a flat top grill if they are compatible. A pizza dome will suit the open grill well. It looks like a chamber with a roof over your pizza. This chamber protects the food from the wind and rain.
Besides, the heat is even in the chamber. You can cook faster with the oven than on the open grill. Grills usually do not have covers, and it will take longer to bake pizza from the bottom to the top.