I'm new to Ubuntu and I recently installed 12.10. Since I'm having problems with online accounts (including Google, which doesn't seem to integrate anything in my OS) I would like to know what exactly a Google account is used for. Does it add GMail into the messaging menu (without gm-notify or similar apps) and syncs my google calendar with the default Ubuntu calendar?
At least for now, online accounts merely help you use the default Empathy chat program to connect with your Facebook, Google Talk, etc. friends. It doesn't sync with GMail or Google Calendar. For instance, you can use Unity Mail for your Gmail accounts, but it requires you to enter GMail account details again as it's not linked to online accounts.
Not entirely certain this answers all of your question ... I use my Google account for consolidating 3 email accounts, then access all three with iMap in Thunderbird; web access too. Additionally Calendar and Google Drive are available. I installed Chromium as a browser so all browser settings are synchronized to my 2 pc's. Additionally the gmail consolidation of calendar and email keeps my iPhone synchronized. Possibly this is all available using FireFox - I just never tried.