No, pizza sauce is not cooked beforehand.
I may have assumed it always is but perhaps some do and some don't. For the places that don't and even if they have their recipe mastered over the years, don't they still like to prepare the sauce (bring all the ingredients together and simmer over heat, i.e. cook it, even just partially) in order to taste a batch for quality control before spreading it on their blank pies?
I've only ever known the sauce to be cooked separately but have learned something new ITT.It can be. Depends on the place and the sauce.