I have tried doing this with limited success. I had a harman Mark III burning nearly wide open, the stove temp was in the 500 degree range, anyway the basement was 90 degrees the cats were sweating, the upstairs was about 70, after cutting a few holes into the floor to get more air moving it didnt make much of a difference. SO, after selling the stove and being tired of hauling coal buckets into the basement and ashes out of the basement, I finished the entire basement.
That was when I noticed something that I should of done from the beginning to get more heat upstairs that is - DRYLOK the basement walls, poured concrete walls suck in so much heat and wastes coal in the process. The basement temp rose 4 degrees just by DRYLOKing the walls, I left an 2" air gap around the perimiter and installed 6mil plastic as a vapor barrier and then studded the walls and insulated them, the basement temp rose 2 more degrees to a steady 65 year round. Anyway, now that all that is done I'd like to try it again but the wife will have no coal dust inside the now finished basement, and frankly, I'd rather not haul it up and down the bilco door anymore either.
The saveings was very little, I was burning a ton of coal a month to save about 150 gallons of oil, so i was only saving about $300 / month in todays money, it wasnt worth the effort to save $1200 per heating season... .... if you want a stove down there just to heat the basement and for nice atmosphere (they flames do look nice when they dance), then it willl work fine and you'll be happy and warm in the basement, but my advice is buy a boiler if you really want to heat the entire house.