The two step app works even with no connection to the internet. I dont know how but it does. I think you dont need to have the same sim card. only the phone turned on.
Google Authenticator uses TOTP (RFC 6238), which means the codes are a function of time plus a secret key. As long as your phone's clock is reasonably accurate, the app will work without any network access.
You definitely don't need network access. I use Google Authenticator on my Wifi only tablet. You need an internet connection to sync it to Google's key but not after that. And, yes, when the tablet's clock is off by a few minutes, the code doesn't work.
