Is Google Authenticator data saved in the google backup cloud? is the Google Authenticator saved with the google backup like wifi passwords, settings, gmail and some other google aps? If I will reflash my current system or make a clean install will it be backed up with all the codes form websites I have there? I do not want to loose it and it will be a lot of work to go to every site I have there, revoke 2step verification and then do it again with new system
Google Authenticator in version 5.00 (as of now) permits backup, but only preferences are backed up, and the critical data (secret keys which creates those codes the user need) are not backed up at all. ADB can also back it up with the command: 

adb backup -keyvalue com.google.android.apps.authenticator2


I'm making this claim based on the presence of the attribute android:allowBackup set to true, and presence of key-value pairs backup provisions in its manifest and a dedicated backup agent is also listed, named com.google.android.apps.authenticator.backup.AuthenticatorBackupAgent. This certainly wasn't the case with prior versions.