I have used toppings many times without precooking them. However, I love the flavor in the precooked toppings best.
The Flat Sweet Onions can be sauteed in butter and some brown sugar, on low heat for about 25 mins or more to get that caramelized flavor.
The Mushrooms cooked in Butter, EVOO, and a little white wine, produces a extra tasty mushroom flavor.
I always precook the sausage, although know a few Pizzeria that put it on the pizza raw and it is cooked as it bakes.
If i am in a hurry to get the pizza made, then i do not cook them, (Except the sausage)