The sub is 5-9/16" deep so your box would need to be about 7.5" deep minimum for wood thickness and magnet clearance. Plus you'd need a little bit of clearance on the front side so the cone is free to move. I'm not sure if you have that kind of depth or not.
You could try mocking something up -- maybe using cardboard.
Volume shouldn't be a problem. CVR 10's will work well in a little less than a cubic foot.