Well first of all the only advantage an affluent background will give you to getting a job at Google is the same advantage it'd give you for any other employer or any other industry (better school growing up, able to focus on that school instead of working, etc).

And we're already presupposing that the person in question is sufficiently hard-working and intelligent that they could be a tenure-track professor at a major research institution. I would argue that the vast of majority of folks in that position could get a very good job at Google provided they had the correct skill set.

And I don't know what part of CS you're most interested in, but my degree is in Political Science and after the first shitty one I haven't had any trouble finding development work in my tiny city.