Extending drywall past finished corner
I think you might have answered your question. Ideally, you want drywall to be supported and secured. You don't want a someone to lean (or even brush) against it, and then you have a torn strip of drywall. Put some wood behind it, make sure that it doesn't move.

For better stability, I would even consider taking an inch or two of drywall off of the corner on the outside, and with a single new piece of drywall, extend as far as you need into the closet space, with new studs behind what overhands the corner. 

Refer to the doodle below. Black being the existing drywall. Red being new drywall. Blue being the frame of the closet doors (usually wood). Brown being the new stud.