Does synchronizing google contacts with apple address book send my data to Apple?
It does not route through Apple. It syncs directly between Google and your computer. The sync icon you're seeing in the menu bar is probably Sync Services (or iSync), not MobileMe. It's simply a visual indication that it is syncing.

The only case where Apple would potentially see any of this data would be in the event of an application crash, and only if it was in the crash report and only if you allowed it to be sent.