I have the Google Authenticator installed on my phone. I notice the codes are generated constantly. It appears the app is running constantly in the background.
Does this app has a major impact on a fully charged android device?
The app is not running in the background. When you start it, it generates codes based on an algorithm tied to your original configuration.
It for sure will not impact your battery, and is not running in the background (the time based codes it creates, are constantly changing though - every 60 seconds - or however long).
But the app is only using resources when it is running, and servicing out the codes to you.
Check the 'battery' section in the settings and see if it shows up there. Also, does it run at startup automatically? Because I'm NOT seeing that on my DROID 4 - it only seems to startup when I use it, and then (like every android app), it hangs around until it gets killed off. Is that what you are seeing?