If you reversed the direction of the fan and direction of the airflow through the duct system, It might be more efficient.
In the arrangement on the show, you have circulating air (the air being moved by the fan) moving in the same direction as chimney gases. So if you had a chimney that was very conductive to heat (another possible efficiency improvement) and was very long, the temperature of the circulating air and chimney air would even out to the same temperature.
If in the same scenario, the circulating gases were moving in the opposite direction to the chimney gases, then the temperature of the circulating gases as it exits the tube tends towards the entrance temperature of the chimney gases. Likewise the exit temperature of the chimney gases would tend towards the entrance temperature of the circulating gases. In a perfect case all the heat from the chimney air could be transferred to the circulating air if the chimney was infinitely long. This arrangement is called a counter flow heat exchanger (since the two gases a flowing in the opposite direction) and would probably be more efficient for the arrangement you had. Although The fan would probably need to work harder to work against natural convection.
Also if you reversed the air flow direction it would pull cool air that sinks towards the floor into the vent to be heated maybe improving the heating effect. If the circulating air also passed through the body of the furnace that would increase the air temperature even more.
So basically, if you simply reverse the direction of air flow through the air duct, it might be more efficient and would be interesting to see the effect it has.
