I think a few million can secure a spot at Harvard, if the student is borderline - say SAT and HS GPA in bottom 25% for Harvard, but not completely outside the range of admitted students. A 2.0 GPA and sub-1000 SAT is not getting in, no matter what you donate.

I know Ivy League athletes with SATs way too low to be admitted for academics (though GPA was good), and they got in. They were big impact players in their sports, and did graduate in four years. Colleges will admit kids with "low" SATs or GPA, but there is a limit, as they want students who can pass courses and graduate. A good guide to admissibility to an Ivy is calculating a student's Academic Index.