Well, there's jazz and jazz. Started out three chord-tricky, got more and more clever dicky till chords had ten notes in and were changing every beat. But then(in some people's hands) it changed in the opposite direction and lost all harmony and became quite modal(eg some later Miles Davis etc etc). And folk is pretty variable too.
Plenty of fine tunes with minor scales(some with minor seconds as well as minor thirds, see reference to "Northern Lass" on the "Beggar Boy" CD thread). But harmonically adventurous? Well, that's down to the musicians who play the tunes. You can go where you like if you are feeling inventive. But in general, no, traditional musicians dont use complex chord sequences, in any culture I am aware of. The complexities of folk music(which are immense) lie in other directions.