Yes, but not that way. You need far more mass than that. You need 2-5 tons of brick around the stove. This will require extra support underneath. 6x6 beams under the affected part of the stove with teleposts should be sufficient.
Google "Russian Stove"; "Masonry stove" or kachelofen.
http://heatkit.com/docs/course.PDF describes using a steel insert into a kachelofen
Another option is a 'rocket stove'. These are made of clay instead of brick, and generally are easier for an amateur to build.
Mart has a good point about basement, although, not quite the right reasons.
I've heard of cases where people have put a wood stove in the basement, expecting the heat to rise thorugh the house. This sort of works, but often results in the basement being way too warm, and the top floor way too cold.
The house my mom grew up in was heated with a wood stove on the main floor, and grated holes in the floor to allow the heat to circulate. (She describes standing over a grate in her night dress getting everything toasty before getting into bed.) But the wash basin on the night stand would freeze some nights.
A thermal mass stove functions in multiple ways:
1. As a radiator. This will not be like the radiators used in lobbies between the inner and outer doors in stores, or like the glowing dull red electric heater, but far more like the oil filled steam-radiator shaped electric heaters, but more so.
These stoves typically have an outer surface between 80 and 100 degrees F -- cool enough that you can put your hand on the outside. Yes there is some radiation, but it's on the order of a hundred watts per square meter.
A conventional iron stove is a much better radiator.
Most of the heat will leave the stove by convection. Air in contact with the stove, warms and rises. This works well for a single well insulated room. It does not work well generally for a house. although an uninsulated partition wall will drop the temp by about half the difference between room and outside. E.g. A bedroom with the door closed when it's 0 outside, and 70 inside will reach equilibrium in the 30's. (the exact temp will depend on proportions of exterior wall, window size, insulation....)
Open designs work well, especially if the thermal mass stove is roughly in the middle of the space.
A ceiling fan moves the heat around faster, and reduces puddles of cold air at the base of windows. Left on low all the time they are frugal with power -- 8-15 watts.)
If you want a more evenly distributed form of heat, apply the rocket stove concept, but use it to heat a large mass of water instead of a pile of masonry. Hot water can be kept in an insulated tank until needed, then used the same way hydronic systems are. This has the advantage that it also can heat your domestic hot water, and during part of the year, the heating can be done with solar thermal collectors.