Sorry for reopening this thread! If i make a normal backup with itunes, it will save my google authenticator codes?
Yes, I think so. You might want to select something about backing up app data. I haven't done it myself, but I have had many apps, with data backed up.
BE CAREFUL: It will save your GA codes encrypted in a way so they can be restored
ON THE SAME PHONE ONLY. If you lose your phone, you cannot restore as far as I know (although admittedly I have not tried). Write down the secret keys as you install them in GA, you cannot do it later.