If you use a phone that doesn't offer back ups of your data, you could be at risk.
Why would you want to? You'd compromise the integrity of the single point of contact authentication. If you encounter a technical issue you have to load your account data onto a new phone. You don't lose all you application data when it's been saved to the cloud.
I don't think you understand what I'm suggesting or how 2 factor authentication works.
2FA doesn't interact with your private keys. 2FA provides an additional, always changing password that you must enter at the point of log in. There's only one location where the ever changing password can be retrieved - your phone or other device. If you have an account-based mobile service (not a pre paid phone) then you have the ability to save your phone's applications regularly to the cloud. If your phone dies you upload your account replication from the cloud and "voila" your 2FA authenticator app is back in your hands.
This has nothing to do with private keys or bitcoin.