How can I set up my Google account without syncing Gmail?
Here's a working solution to add a Google account and prevent it from syncing everything.


Before adding the Google account, disable Sync (from system settings
or from your pull-down menu).
With sync disabled, add the Google account.
Enable Airplane mode to prevent all data transfer.
Enable Sync. You must do this to modify the specific sync settings next. 
Go into sync settings for the Google account, and uncheck all services you don't want synced. For your case, you only want Sync App Data enabled.
Disable airplane mode.


You now have the google account on your phone, and it hasn't synced anything except the services you chose to let it sync. 

I follow this procedure to prevent emails and contacts from syncing. Contacts in particular are very annoying, since disabling sync doesn't delete the synced contacts from the phone, so you must prevent them from getting on your phone in the first place with this solution.