I think the answer must be no.However if you booked a jazz band for a folk festival and didn't tell people what genre.........
Going back to improvisation, you are no doubt right Ian in that most music would have a degree of it whether because of forgotton notes, or similar. When I used to play trad, the improvised solo was fundamental. If you could n't improvise - you couldn't play jazz. None of the folky stuff I play nowadays (sessions or morris or ceilidhs) has improvisation as the basis of the music.
In order for trad jazz to be part ofthe scene, the labels have gotto come off.