The QR code is displayed on the unsecure connected computer. Your phone network is used to perform the login, so it very little data.
A logical next step would be an app that can streamline the auth a bit (have your username prefilled from the Android account) and send the auth to Google via SMS (often easier and cheaper than getting started with dataroaming).
If you are overseas, roaming costs are crazy. I'd consider paying them to download a single .png (QRCode) and then use an untrusted computer.