Can I wipe my phone even if I use it for 2-step verification? I fear that if I reset my phone to factory defaults I'll never be able to access my Google Account again, since I use the Google Authentication app on it to provide the 2nd step of the verification.

Am I right? Should I remain worried?
There are several ways to address your concerns.

First - you should print the emergency codes. Google has good directions on how to do so here. (reproduced here)


Sign in to your accounts at https://www.google.com/accounts/SmsAuthConfig.
Look for the “Printable backup codes” area.
Click Show/Generate codes.
If you are fine using the current set of backup codes, you can print or download them. If you believe this set of codes might have been stolen or you’ve used many of the backup codes, you can generate a new set by clicking Generate new codes.




Second - Even without backup codes, you should have supplied your phone number to Google at some point; this allows for you to have a temporary code sent to you in a text message. As shown in the following image:



Thirdly - You can disable 2-step verification while Wiping your phone, and re-enable it again after completion. (This requires you to set everything back up). Google Instruction Page to Disable 2-Step Verification (steps reproduced here)


Visit the Using 2-step verification  page under your Google Account settings. Sign in with your username, password, and verification code if prompted.
Click Turn off 2-step verification.
A pop-up window will appear to confirm that you want to turn off 2-step verification. Click OK.