The Klingons and the Maquis did work together. The Klingons furnished for the Maquis numerous cloaking devices as Martok tells us when warning Sisko that Eddington's alleged doomsday missile is most probably cloaked. So, yes, there was active cooperation between the two. Kurn objected to the Cardassian invasion but could subsequently changed his mind given his realisation of the full ramifications of his decision. That can plausibly happen.
Before the Dominion struck in a three day blitz that took out the Maquis, Eddington had become quite a legend in filling the vacuum that the weakened Cardassians had left. It's not hard to imagine Kurn performing similar feats given his expertise.
Kurn's house is gone but a feasible route back is to do as Worf did; get adopted by a Klingon who knows of Kurn, perhaps sympathised with him in his fall and admired his feats in battle. Kurn gets his honour back. That's what matters to the guy more than power.
The writers had Dukat plodding along in some dilapidated freighter and then had him running Cardassia a few episodes later. Kurn, at a loose end, joining the Maquis is less of a writing leap than that.
Thanks for letting me know about the Klingon-Maquis alliance. I don't even remember that. Sure the writers could come up with something to put Kurn in the Maquis fight, I just don't see that happening from what we saw of the character. That doesn't mean it couldn't happen if the writers came up with something. Hopefully it would have been something good.
But from what I saw of Kurn I don't see him seeing the Maquis fight as his fight. And yes he cared about personal honor, but he also cared about restoring his house, and having a powerful house would be important to him. Perhaps he might equate power with virtue or honor, but I'm reaching there with that one. I do agree he would care more about honor than power, but then again, I can't say political calculation would be completely tossed out. I did a check of Memory Beta and at one point Kurn was plotting a coup to prevent Gowron or the House of Duras from gaining power and Worf did use Kurn's forces as a bargaining chip with Gowron during the Civil War, with Kurn's consent-forced, reluctant, or otherwise. And I still believe that Kurn would care more about actions that restore his house and his honor within the Empire. And maybe even return to a position on the High Council. Why would the Klingons care about the actions, no matter how heroic, of the Maquis? How does that get him back what he lost?
That being said, once I took a look at Memory Beta to reacquaint myself with Kurn I had forgotten that he took a position with the Bajoran Militia. That doesn't really strike me as something he would do, however he was pretty much at wit's end at that point. So for him to go Maquis I could see the writer's putting him in a place where he had fallen so deeply and all he cared about was fighting. It didn't really matter who. Honor had been denied him and likely would never be restored. If they did that, it could even set up a redemption arc for him that DS9 cheated him out of.
But to the point of Kurn being on Voyager, I think his presence might have taken away from him ultimately. I mean I don't to see him assimilating into the crew. Part of what made him unique on TNG was that he didn't assimilate, or did so in a backhanded manner-though admittedly much of his consternation or jibes were designed to test Worf. Having him on Voyager, for seven years, I think his character would've been whittled away. I like the idea of having a Maquis counterpoint (like Chakotay or I imagine Ro, Tom Riker, or Eddington) would could be opposed based on ideological grounds. Granted Kurn could also have an ideological beef with the Federation, but it just seems like adding extra baggage to a character already laden with a potentially rich backstory.