I can't see that is getting you any great improvement in efficiency. On the other hand looping the exhaust back through, in effect consuming the flammable gasses that would be otherwise lost up the chimney, is a proven way of improving efficiency. Catalytic converters do it in a slightly different manner but the idea, consuming and extracting heat from gasses that would be lost, is largely the same.

In addition to getting more heat from a cord of wood reburned or catalyzed exhaust gasses carry far less creosote, soot and smoke. Which means the chimney doesn't have to be cleaned as often, your not dropping black clumps on your car, and the air stays cleaner. All good.