Beauregard lifts Bobo a few times, and he's even seen without his hat (was the puppet ever shown hatless? The figure had a removable hat).
Sure, I've seen Beauregard take his hat off at least twice on the Muppet Show. Once was when he shyly asked Crystal Gayle if he could have her autograph.
Crystal Gayle: You sure can. [Takes the paper he's holding and signs it.] There you go.
[Beauregard puts his hat on and takes the paper back.]
Beauregard: Okay, thank...Hey, wait, this is no good! It's upside-down.
Crystal Gayle [turning it right-side-up]: How's that?
[Beauregard stares at the paper in amazement.]
Beauregard: How did you do that?
http://vodpod.com/watch/465239-crystal-gayle-her-muppets-show
Here's a clip with that exchange, as well as some other moments from the Crystal Gayle episode.