Should I disable Google contacts in my Mac System Preferences?

Yes.  The Contacts Sync app works best when it syncs your Google contacts with either iCloud or Mac.  With your iCloud or Mac contacts containing the same contacts as your Google account, there is no need for your Google contacts to be enabled in your Mac System Preferences.  Having it enabled may even lead to duplicates.

To disable it, go to your Mac System Preferences > Internet Accounts, find your Google account, and turn off "Contacts."

Video showing how to disable a Google contacts account with Mac OS X 10.9: