Yes, employers propably do google the possible employee before hiring, but unless you've done (or been accused of) something grandiose, you should be safe.. unless you have very odd name that isn't common.

Now I live in Finland and my full name isn't that common. But as it just happens to be, there lives not one, but two guys who share my FULL name and live in the same part of country too. So if someone ought to google based on my name and location, they would find out that I've been a police chief and also have masters in CS, yay.