I'm not going to shit on a study I haven't read, but it seems likely that if you come from a "rich" family capable of buying you into a college via back channels, you've probably already got a pretty solid leg up in the game. I can't imagine correcting for all of those variables in a manner which isn't going to leave at least a
few questions.
Either way, I'm sure having a diploma from Harvard would open some doors for pretty much anyone, and I'm not naïve enough to pretend otherwise, but I have serious doubts that a diploma from Harvard can truly tell you anything other than that person has the ability to make it through Harvards' admission filter, and do mindless homework for X number of years, like every other college.