I tried it just now to be sure. You need the authenticator number to log into account management too, so it should be as safe as the game. And as I read the instructions, you need to phone them if you lose the authenticator and provide lots of details before they will release the account from the authenticator binding.
A lot depends on the eddress of record, so keeping control of one's email account matters. I suppose a keylogger could gather that information too, so nothing is perfectly safe.
Account Management Page
You need the authenticator number to log into account management too, so it should be as safe as the game.
And as I read the instructions, you need to phone them if you lose the authenticator and provide lots of details before they will release the account from the authenticator binding.
A lot depends on the eddress of record, so keeping control of one's email account matters. I suppose a keylogger could gather that information too, so nothing is perfectly safe.