Ideally, yes; practically, no. The point of admissions has become to determine that admitting a given student will do one of three things: Benefit the school

Ideally, yes; practically, no. The point of admissions has become to determine that admitting a given student will do one of three things: Benefit the school through future press from stand-outs, alumni donations, and better GPA, SAT, and ACT stats in the various rankings (all leading to more enrollment in the future), benefit the school by paying to attend and not really affecting rankings, or whether they can pay and not really hurt ranks that badly. And the number of free admissions to most areas of undergraduate study is 0. Full-ride scholarships are usually athletic, not scholastic, but most partial scholarships are based on test scores and apply regardless of the course of study.