You may synchronice your iPhone with your Google account by following the Google instruccions. It has to be the default approach to this issue. It may seems peculiar but following Google instructions you’re going to set an Exchange account. You’ll get a full Google account sync except Notes.
I remember the first time I try it they where since I just configure my access as an Imap access.
So If you want to sync, also, your notes, let apply a trick; configure one more account but, when add this new account choose Google -not Exchange- and type the same user and password you’ve set in your former configuration. When you are able to choose what to sync, avoid Mail and Contacs and just choose Notes.