To make sure you don't get locked out, before you upgrade you'll want to write down your restore code: from the app menu, click setup and then continue. You'll have a serial number and a restore code here which you can write down or take a screenshot of for reference. Then, if your new app isn't working, open the menu, click restore, then "I want to perform a restoration," then enter your serial number and restore code. If you haven't already, you can also set up SMS protect, which allows you to remove a broken authenticator -- or broken authenticator app, in this case -- from your account via a text message to your phone, so you can detach the old authenticator and connect a new one.
Anyone who has their iPhone set to automatically update apps should be especially wary, as this means your authenticator app will update as soon as the update appears on iTunes. Make sure you're ready for the update so you don't get locked out!