IRC Building- Building shall mean any one and two family dwelling or portion thereof, including townhouses, that is used, or designed or intended to be used for human habitation, for living, sleeping, cooking, eating purposes, or any combination thereof, and SHALL INCLUDE ACCESSORY STRUCTURES THERETO.
IBC and UBC - Any structure used or intended for supporting or sheltering any use or occupancy.
So under any of the codes, I would have to say that the sunroom would be a building with habitable space if it's freestanding and a part of a building with habitable space if it's attached. Anyway, that's how I read it, but I am not an expert by any means.
Also, you need to determine which code is adopted in your area and if there are any local changes to the code.
Of course, you could hang a closet rod all the way across and call it a closet, or put a toilet in it and have a wonderful view of the area while doing your business. At least it'll get the neighbors talking.
Bob