Uh, I don’t think so. Most engineering and nursing schools that I know realize that they have lock-step program with class sizes capped, so they limit the admissions to the program in the first place.
Actually, most will drop out of pre-health after getting C’s Gen Chem and Calc 1. 
…but the broader point is that pre-pharm like premed (and pre-dent) can major in anything; many major in English or History. And, how many publics actually consider intended major to the College of Arts/Letters & Sciences?
But note, even the top privates have capped classes. Only Harvard has the money to open another section/class with just one student, bcos the seminar in the next classroom is capped at 15.