I honestly think if JL features MM he will be one of the most popular characters. Seriously he has the best powers first of all. Strength rivaling Superman's, flight, telepathy, shapeshifting abilities into ANYTHING, and invisibility/intangibility.
Martian Manhunter's move where he phases his hand through someone's body using intangibility, then he phases back, and there's a hand inside someone's body. That move would be so badass on screen.
Martian Manhunter deserves his own film after a JL appearance. I think he could carry it after exposure from JL.
It would be a mixture of scifi and noir. Someone described Dark City for the tone, I think that's perfect.
If WB would use parts of J'onn's story on the animated series, at least for the Mars scenes, it could be awesome on screen. It would start off like a space war epic, and would establish J'onn, a father and husband, as the leader of a rebellion against the evil White Martians. Ma'alefa'ak wasn't in the animated series, but I would probably feature him too, maybe he could betray his brother on Mars. But ultimately, J'onn would be the only survivor on Mars, but he is able to defeat the White Martians, and traps them on Mars. After the victory against the White Martians and the death of his family, J'onn decides he can't stay on Mars, and comes to the closest habitable planet Earth, and disguises himself as a detective in Gotham City. After some time operating under the radar, the US Government sends a ship to Mars, and like the cartoon, the astronauts unleash the trapped White Martians. The Astronauts return to Earth, but they've been replaced by Ma'alefa'ak and the leader of the White Martians. I wouldn't go full out invasion, but I would make the story about J'onn tracking down and defeating the disguised martians.