Audio CDs do not contain filesystems as such, so they can't be mounted. And no, you don't have to rip CDs in order to play them. Where did you get that misconception? All you need is a player that can read cda data straight from the CD drive. This includes most of the major ones, including audacious.
But you're going about it all wrong trying to use the file browser to load it. Audacious has a separate CD input plugin that accesses the drive directly. The function is accessed through the menu option called "plugin services", which should show up on all your right click menus or when you click on the "add files" button. If it doesn't work, go to your input plugins config and make sure the "CD Audio Plugin" is configured for the correct device. If you don't have it at all, then either your version of audacious wasn't compiled with CD support, or something is keeping the plugin from loading.
P.S. The error message you're getting at the end has nothing to do with your attempted CD playback. It's showing up because you're trying to run audacious as root. It's not finding a default playlist in your /root directory (probably because you've never used the program as root before), so it spits out an "error"--but it's really just an informative message in this case.
In any case, you generally shouldn't run programs as root unless absolutely necessary, and playing an audio CD does not fall into that category.