General surgery is a backdoor into plastic surgery and, fortunately, general surgery is moderately competitive (i.e., it's quite likely that an average student would match into a residency program). So you can match into a good university g. surg program from ANY medical school.
The prestige factor becomes significant in the Match for highly competitive specialties at renowned hospitals--ENT, plastic surgery, ophthalmology, dermatology, neurosurgery, and orthopaedics. If you want to do your residency in orthopaedics at Mass General Hospital, then you'd better attend a prestigious med school. Otherwise, it really doesn't matter. Graduates from every med school in the country become academics; take a look at the faculty lists for any med school--you'll see people who graduated from a wide variety of med schools (including the "unranked" ones). Similarly, med students from every med school match into the highly competitive specialties mentioned above, but grads from lesser known med schools typically do not match at renowned hospitals in these specialties. Nonetheless, such students live highly productive and succcessful professional lives--their incomes and patient interactions certainly do not suffer from the lack of an ultra-prestigious institutional background.