Evil character cannot 'gain' a good brigade, though I suppose they could get a church identifier. Obviously, Faithful Leaders is intended to work when someone is converted to a Hero, but you have hit on a great combination.
"Gaining" a good brigade is not something that works, IMO, since it cannot have both the evil brigade and Clay, and it is "gaining" it not "becoming" it. However, I'd have to say that (as written) the EC would be taken to territory and it gains the church identifier...before it is taken, though, they'd have SI to play (though in the new brigade).
Any other Elder want to weigh in on this one?