[henhouse]

You should be able to, yes. Google Authenticator is pretty basic where it's simply scanning a QR code to get the TOTP token and storing that locally. It's apps like Authy which screw you over by forcing you to use them and ONLY them for 2FA for websites who opt to use it in their service. They don't make it possible (iirc) to get the token out so you can use your preferred authenticator app.

But back to your point: I used to backup to Google Authenticator and LastPass's Authenticator to prevent me from losing access when I migrated to a new iPhone since they don't backup. They both worked just fine interchangeably.