There's lots of trouble without certain Google things.
But, you can root. Get titanium backup and freeze Google apps. ONLY the obvious ones, nothing system related. Or you'll be in a mess.
I don't even know if phone can be frozen. I kinda doubt it.
But....you can use a launcher, like Nova and get rid of all the icons you don't wanna see. And hide them from app drawer too.
That's about all you can do.