Does Adobe Premiere Pro CS6 have a fullscreen mode?
I'm fairly certain there is no such mode.  It doesn't have the same kind of feature that lightroom does as the full screen video preview is really the closest in terms of being related functionality.  

The full screen mode is helpful in Lightroom because it allows focusing on the photo with only basic controls.  Premiere is much more complex than LR and a significant portion of screen real-estate is taken up by those controls.  If you aren't purely focusing on the video, then the amount of lost and distracting space really isn't a big issue.

Note that if you really need every last scrap of screen real estate though, you can adjust the task bar so that you can make it only a small line on the bottom of the screen though.  You really are not practically losing any meaningful amount of screen real-estate.

The only functionality is the functionality that maximizes a particular panel or full screens the preview, but you already mentioned those are not what you are looking for.  That's the closest you are going to get though.