I think that there is a helpful role here for the organizer. The organizer can check in with touring bands, say that some of the local musicians are always looking for chances to sit in with visitors, and ask the touring bands what they are comfortable with. This actually makes it easier on the touring band, because if they would rather not, it's a lot easier to say that to the third-party organizer than it is to say it to the musicians directly. It also allows them to ask some questions that are harder to ask a musician directly -- "well, how good is she?" I suspect many bands will say sure, for a dance or two. Those that won't are likely going to be bands with carefully scripted arrangements that are hard to convey to others on the fly.
I think questions of when and how, on mic or off mic, and number of sets should be totally at the discretion of the band hired for the evening. An organizer trying to dictate any of those things would be seen as going outside his/her sphere of influence. (Though the sound tech has to know what is going on and may have some limitations on what is technically feasible.)
David