For me, iOS 11.1 did not brick my phone. It made it unusable in a variety of amusing ways, but it didn't brick it.
The main issue I had was similar to yours - Google Authenticator had been completely wiped clean.
Thankfully, my iPhone backs up every night so I lost less than 1 days information (and no photos). This included restoring my Google Authenticator to a fully functional state - so the answer to your question is yes, your Google Authenticator information is stored in iCloud backups.
It also turned out that I had no recovery codes for my various accounts. I have 11 accounts in my Google Authenticator app - including Cloud Flare and Teamviewer. Neither of these apps have a backup 2FA method (like a text, a phone call or similar) - and Teamviewer do not offer any official support to free accounts. This meant I was locked out of my Teamviewer account permanently.
I can't stress this enough: ensure you have your backup codes stored somewhere - somewhere safe:
Personally I've put them in my password manager, but the Notes app on your iPhone is also perfect for this - or print them out and file them somewhere you won't forget. I'm also considering disabling 2FA login to Teamviewer.