Still doesn't play nice (i.e. work at all) if Google Authenticator is installed. Never registers.
According to the market, GA has between 50,000 and 250,000 downloads, so I don't think it's merely a niche app.
Again, I'm running a stock Optimus V, unrooted. GrooveIP worked fine prior to installing GA, now it doesn't. When I installed GA, I was required to re-log into the other apps that rely on my gmail and/or gvoice accounts, using new passwords from within gmail. This app didn't require that. Therefore, I'm guessing that it's still trying to login with my old credentials and that's why it's not registering.
Before you respond to this post, please ensure you've at least tested GA, otherwise you won't really understand what I'm talking about.
Here's additional info about GA:
Google Authenticator - Google Apps Help
Installing Google Authenticator : Turning on 2-step verification - Accounts Help
Before you respond that GA isn't necessary, see these:
PSA: Now’s a Good Time to Change Your Gmail Password [Hackers] | Android Headlines
Google: Hundreds of Gmail accounts hacked, including some senior U.S. government officials - Post Tech - The Washington Post
Alternatively, just google "hack gmail password".