Don't think you need the authenticator for Gmail. I have two-factor turned on and all I had to do was generate app-specific passwords for my Mac and iOS devices. Can't remember if I needed to re-add the Gmail accounts or if I got prompted to enter a password, at which point I entered the app-specific passwords (last generated for iOS back in 2014).
Worst case scenario, might have to remove the accounts and re-add them, but since Gmail is IMAP, won't lose anything. But may be painfully slow to download all your e-mail to the device again.