No, seriously: It doesn't matter. People manage to succeed with pitiful little CWRU degrees like my own. And, obviously, many of the most successful people in the industry never went to college at all.
I have heard the occasional rumor that Google is obsessed with academic credentials. If true, that is more of a problem for them than for you.
... since hiring the guy that went on to create Gmail!
Yes, this reminds me of what tends to happen as companies get larger: they add more processes and "standards" and management and therefore increasingly lose out on the kinds of opportunities and people they used to be able to get.
Granted, Google stands out as seeming to do pretty well fighting against it, staying fairly "agile" for it's size and age. But if your company reaches the point where it cares more about what university you attended rather than your intellectual qualities and accomplishments, you're heading in a bad direction.