This may surprise you:
[Students who don’t submit SAT scores when they apply to university], with significantly lower SATs, earn [university] G.P.A.’s that are within five one-hundredths of a G.P.A. point of submitters, and graduate at rates within one-tenth of 1 percent of submitters.
This comes from the former head of admissions at Bates College, in Maine, USA, but presumably would be generally true.