I just finished getting Wabbajack from Sheogorath. In one of the scenarios (not specifying just in case someone has not done this yet), there is a chest (behind Palagius' bed) that looks like I can interact with it, but does nothing when I click on it. Is this normal, or am I missing something in this quest?

I think it's normal In that quest you can't open your inventory while your there so my guess would be the same for the chest.

That's a good point. You cannot open any menu (except possibly the game menu) while there. So the chest is just a tease, then