Ivies give so much need based scholarships that athletic scholarships aren't required. If someone's parents and poor, the school finds a way for them to graduate debt-free. (This is a big plus for them)
As for sports having an impact... They may not let in a 900 SAT football player, but 1200 may be enough for an Olympic rower.
1: http://www.ivyleaguesports.com/information/psa/index