No, Dave's reaction gave it away - the way he was laughing and playing early on. It was immediately clear like 3 questions into the interview something was up, and Dave wouldn't have kept that up otherwise. It was definitely some business, of what I'm not sure, and how "in on it" Dave was is debatable, but this wasn't a Dave vs Cher moment at all. When Dave hates someone, he makes no qualms or jokes about it, at least not like he was last night, he'll just shit on someone flat out.
Remember, nobody hates celebrities like David Michael Letterman, nobody.