Interesting idea. But I'd say, if you want to replicate a favorite pizzeria's dough, you're better off finding out their recipe, or trying to figure it out if they won't tell you. Or just buy dough from them! Because theirs is probably not sourdough. Doing what you outlined above will result in sourdough, eventually, or it might just die. Either way it won't taste like their dough. Although it might be a fun experiment anyway.