So I was about to google "does mister poopy butthole have a poopy butthole" to see what interesting discussions the fine gentlemen of the internets might be having about said subject. However, right before pressing enter (and I am not joking, i typed in the entire thing) I had a revelation.

Specifically, in the episode where Rick drops Jerry off at Jerryburee, as the space ship does some thing the three mind mend (Jerry, Rick and the big white thing guy). At some point, you hear Rick saying "I have shit on my ass".

Now, here comes the defining moment, gentlemen. You see, it's NOT Rick that has shit on his ass. It's Mister Poopy Butthole! It's merely that because Rick -IS- Mister Poopy Butthole at this time, that he has felt the shit on his ass.

Hence, I consider my question answered. Mister Poopy Butthole does tend to at least generally, if not always, have poop on his butthole, as the name implies.