Pizza on BBQ working ?

I'd put it onto some foil then onto the bbq grill, to prevent charring the bottom before the rest of it was cooked.

sure. Turn gas grill way down, plop pizza on the grill and close the lid and cook till crust is done and cheese is melted.
If its a charcol BBq, wait till the coals are not so bright red hot and plop pizza in the grill and close the lid and cook till crust is done and cheese is melted.
Everything on a frozen pizza is already cooked so all you are doing it heating it and melting the cheese.

If it is not too greased up with pork/beef fat it will work just fine, lots of recipes for cooking homemade pizza on a grill because they heat-up higher than kitchen ovens.