Short answer, no. Employment and wage statistics suggest that simply completing a 4 year course at an accredited school is sufficient to put you into the much smaller unemployment pool. Additionally major has a bigger impact that 'eliteness.'
That said, we were at the College recruiting fair this past spring helping out and one of the problems is that kids from disadvantaged familys do not even apply when they might be successful on the reasoning "Well if I got in, I couldn't afford it so why waste my time?"
We suggested to the representatives from Princeton, Ohio Wesleyn, USC. Stanford, and Brown (and any people we could talk to) that they make visible ways to apply without paying any fees for these kids. We have to make it at least a no-risk proposition for them to apply, in order to get them into the system in the first place. On the proactive side one of the parents was reaching out to the Bill and Melinda Gates trust to see about an application scholarship fund (basically fronting the application cost).