Unless you can afford it without living in the shed, I wouldn't touch it. If you rented it, and then someone (like the tenant) reported you living in the illegal shed, and you got kicked out, you would be in trouble.
I should mention that the chances of getting the shed legally zoned are pretty small. If there were good odds, the property would have been gobbled up by now.
Does this help solve the mystery?
Sold AS IS. Three level 1904 house is in worse condition inside than it looks from outside. Located on a corner lot near busy Glebe & Walter Reed Roads. Clutter & old furniture stored inside. Dated kitchen & bathrooms. Upper level rooms have water damaged ceilings. Window a/c units. Narrow stairs access to walk out basement. Basement needs work. Large newer shed is an annexe that is a one bedroom house. Large tree in middle of fenced backyard. Shows poorly.