I fully support the idea of taking Minthara prisoner on a Good run, but she should be able to get out of the cage and become a companion (optional)
I doubt Minthara would have any interest in joining a group that imprisoned her. She's a Lolth-sworn Drow, and from what we've seen she's an extremely proud personality, and fierce warrior. She would probably rather die in the name of the Absolute like a true zealot than join the campaign at that point.
I will say it might be fun to have her try and persuade us with her illithid power to set her free or join her.