Yup. I keep a cheap backup Android phone with Google Authenticator installed just for this purpose. Every time I add a 2FA code, I add it to the backup phone. I also print out the QR code, but a backup phone is far more convenient.

I dropped my main phone into the toilet a week ago, completely fried it. Moved the SIM card to my backup phone, and carried on like almost nothing happened. I then powered up my 10-year old Nexus 7 tablet, and duplicated all my 2FA codes to the tablet. When I get a new replacement phone, I will duplicate my 2FA codes again.