Yeah, I think it would only seem off-kilter b/c we've never actually seen him commit crimes of a sexual nature in the regular DCU.
BUT, if it was "funny" to him? I think he'd do it, for sure.
And I agree, other than a few things, I wasn't really thinking: wow, Azzarello's Joker is soooo much like the Dark Knight Joker. They're different. (Which is a very interesting aspect of the Joker in that he can be interpreted in all these different ways)