I'm pretty sure I could improvise very well on jazz. Just a matter of learning the chord changes. My hands do what they feel like doing and it usually sounds pretty good to me, although my standards may be low. I just tried it using Bebop style on the PA3X with That Old Black Magic and Route 66, probably not true jazz songs, but I know them at least.
I just play the notes that sound right and skip the ones that don't.
DonM