It seemed like such a good idea until it was tested.
Some building codes in North America require that woodburning equipment have a supply of combustion air provided from outside the dwelling. These rules were put in place on the assumptions that most smoke spillage from wood stoves, fireplaces, furnaces and so on is caused by their inability to "get enough air" and that the outdoor air supply would provide enough air and therefore reduce spillage.
In 1989, when Canada Mortgage and Housing Corporation published the report of an ambitious laboratory research project, the results made clear that both assumptions were wrong. It turns out that most smoke spillage from woodburning systems is caused by bad system design and that outdoor air supplies don't do much of anything to reduce spillage.
The question of how to supply combustion air to wood burning appliances is complex and difficult, and made harder to understand by the fact that the scientific findings on the behavior of outdoor air supplies tend to contradict the normal assumptions that people make.
The articles in the left column offer a basic explanation of why outdoor air supplies, whether directly ducted to the combustion chamber or indirectly to the room the appliance is in, don't reliably improve performance or reduce smoke spillage into the room.