Yes, Google has a linux distribution it uses for desktops.
Yes, it’s called Gubuntu (a prize for anyone who can guess which other distribution it might be based on 🙂

For those of you in SoCal, Vince Busam, a current Google systems engineer will be giving a talk on Google’s use of Linux on the desktop as the USC LUG on Feb 23rd 2006. Details here.

No, there are no plans that I know of to release Gubuntu to the public 🙂