I can't answer for each and every parochial school but yes they do. About 1/5 of the students overall are non-Catholics according to what I read and some have more non-Catholics than Catholics. Schools are pretty much secular today. In some schools, there are as many as 80% that are non-Catholic students.

I would guess that one of the prime reasons a non-Catholic parent would choose to send their child would be safety and discipline. Misbehavior isn't tolerated and a kid acting out would be quickly expelled if they couldn't be reined in.