Well, it goes both ways, doesn't it? Few jazz players have the required feel for a rock groove. Vinnie C. can do it, Gregg Bissonette can do it and a few others can do it, but in general, we'll always be better at one "style". You can usually tell where someone is coming from when you hear them play in a different setting (fusion players attempting a solid backbeat is very often... amusing).
Absolutely, and it was a big point in my discussion elsewhere. Model your blast beats after Derek Roddy, but find another hero if you're wanting to learn swing.