BTC-e Two-Factor Authentication: Saving the Code

[GSnak]

I frequently change ROMs on my phone and need to be able to add the BTC-e key easily so as not to lock myself out of my own account. I screencapped/printed the QR code as well as saved the keys themselves to a text file. I successfully used Authenticator to scan the QR code on the printout and generate the verification code to log into BTC-e. Can I now wipe and/or lose my phone and I'll be able to use this printout to configure Authenticator on the new ROM?