Yep! Hence The Google auth app was widely recommended before when there's not that much good alternatives. As with a rooted phone + Titanium backup, that's what I did in the past too. It's nice to have in-app password encryption though; just a small extra layer of security.

If you're going to switch over and you have a rooted phone, switching over is going to be A LOT easier. Aegis has an "import from app" feature if you have a rooted phone. It can grab the backup codes off Google auth. I suggest trying it out.