Whilst they might not have a case, I suspect Google's lawyers would be after you fairly quickly if you developed that domain. Even if that didn't turn out to be the case, I can't really see the domain having any value for two reasons: 1. It's too easy to confuse 0 and O - people will almost certainly type one of the first three characters incorrectly. 2. How do you pronounce the name? 'Zero oogle'? You'd need to register zerooogle.com as well then, and probably zeroogle.com and zeroooogle.com for people who mis-type the number of o's.
I would personally stuggle to remember it. Constantly asking myself how many 0 and how many o s!! lol
0 is far away from "G" on keyboard. But you might still got typo errors for your domain. I also think reg fees to low $xx.