It depends. If it is something that I like (and can eat, as a vegetarian) then probably yes. If it is something that I don’t like, or can’t eat as a vegetarian, then I definitely would not.
If the pizza restaurant only served cheese pizza, then most likely I would eat there. If they only served pepperoni pizza, I would not.
I remember one time, my friends and I went to Lake Havasu on a little weekend retreat. We saw what appeared to be a cute little pizza place overlooking the lake. It was the first, and only time I ever encountered a restaurant that made their pizza with meat sauce (only). There was no option of just plain marinara sauce. We ended up going elsewhere.