Not really. To frame it out you would need to use 2x4 or 2x3. Add in the sheetrock thickness on top and now it is only 5 to 6 inches deep at most. That's not a lot of depth. It sounds like a good area to put shelves or a built in with shelving. I know if I saw a closet in a house like that I would wonder why it is there.
I think @Henry's idea is the best. A curtain and hooks on the wall are temporary and could easily be removed.
Another idea is to reclaim some of the room and built a full size closet using the extra depth that is already there.
