I work at Google and I am an engineering-degree dropout who was referred by a music-degree dropout; we both now report to a VP who was a mathematics-degree dropout.
That's not to say it won't be harder to get past resume screens and such, and a referral does help in these cases. Thetrumanshow is right that Google suffers when people like you don't apply.
Strangely enough, being a dropout sounds sexier than having a BA in English! This all happened waaaay back in 2007 when my resume wasn't as impressive. Since then I've really fleshed it out, and I can get hired places on the strength of my accomplishments regardless of what I studied a decade ago. It's too bad working for Google doesn't sound as appealing now as it did in 2007, or I might just try applying.
That's not to say it won't be harder to get past resume screens and such, and a referral does help in these cases. Thetrumanshow is right that Google suffers when people like you don't apply.