Some of them, yes. But definitely not all. I like The Chipmunk Song, Grandma Got Run Over by a Reindeer (yes, I actually LIKE this one!), 12 Pains of Christmas to name a few. There was another one they used to play all the time (back when it was new) that they haven't played since, I think it was called "Rust and Smoke" and it was about a guy driving his beat up rusty Chevrolet sung to the tune of Jingle Bells. I loved that one!
I DO NOT like the hippopotamus one, two front teeth, or anything "sung" by barking dogs or meowing cats.
One year I saw Sirius had a "Comedy Christmas" station, don't know if they still have it, but it was pretty much nothing but these weird novelty holiday songs/sketches. I heard the Mackenzie Brothers 12 Days one on there ("and a beer!"), also remember some really bizarre version of Jingle Bells with Mel Blanc doing a fake Swedish accent (not to be confused with his "German" Yah Das Ist Ein Christmas Tree).