It would take awhile to heat up for sure. Insulate the floor well enough and I think it could work. How would you bring the hot air into the floor? I am installing an earthen floor in a 20 x 20 space currently and have wondered about heating the slab from the stove. There is a
video, perhaps one of Paul's, that shows a heated slab with radiant heat via copper tubing wrapped around the stove pipe. My intuition is that using radiant tubing style systems are more efficient, not sure though. Either system will utilize electrical pumps/blower. I think by the time you design and install the system you will have lots of parts both electrical and mechanical. Instead you could install inexpensive electrical heating cable made for floors under your flooring. If the slab is insulated really well this would be far simpler and would achieve the results desired, warm feet. A 20 X 20 space is small, a
wood stove would easily heat the room. Making you feel warm and happy that you did not go to all the trouble.
I say more power to you if you figure it out and it is efficient though. I am always thinking of ways to heat, it is winter. For now I use a woodstove and sweaters!