Just one data point, but as a former low SES admit to a highly selective college (although certainly not Yale level) I can say absolutely that going to a school with the money and resources to help a kid not used to some of the really basic rules of education that most upper middle class and higher kids (including my own) learn early helped me get through and graduate.
I think people sometimes misinterpret some of the academic challenges faced by low SES kids from crappy high schools who head off to college. I am not talking about the relative difference in academic rigor between Bucknell (where I attended) and a local state school, but just basic things like learning that you have to show up for class regularly, how to take notes, the need to do your work regularly, or how to study. In my high school, no one cared if I showed up for class, because I was smart enough to do well on the tests and didn’t create problems for the teacher (well, the last may not be absolutely true). I certainly never took a note in my life, and a particular point of pride was that I did not take a single school book out of my locker for my entire senior year. This behavior was not unusual in my high school, and I guarantee it is not unusual in bottom performing urban (probably suburban and rural too) high schools now. In fact, things are likely worse. I don’t think people realize how truly terrible some of our public high schools are compared to the schools most of our kids attend.
In any event, the challenges I outlined above will hit the low SES kid whether he is at Amherst or Univ of Akron. I know plenty of kids (athletes and non athletes) who went to our state universities and fumbled around for a quarter or three before dropping out or being kicked out because they didn’t have the tools necessary to succeed and/or know how to access the support network to get them help. The benefit of a smaller, more elite school is that there is a greater chance the kid is helped by the ever-present academic advising, reaches out to the myriad tutoring services available, or that a prof in one of his generally much smaller classes takes an interest and extends a hand.
Its not just about who took the most APs (I didn’t even know what AP was when I got to college) or who went to the science olympiad.