same thing as if you didn't have an oak at all.
I assume that by "normal furnace", you mean a forced hot air system. the cold air returns for these systems aren't for feeding the combustion in the furnace; they're to re-circulate the cold air in the house so that it gets heated, and re-distributed.
the combustion air that feeds the fire in either a furnace, or a pellet stove, gets "polluted" by the fire, and has to be sent out the chimney. In both cases, (A pellet stove really isn't a "stove"; it is really a wood-fired furnace that looks like a stove), if the combustion air is drawn from inside the house, (ANYwhere inside the house), it has to be replaced by air that is outside the house. With an oak, that air is isolated from the rest of the air in the house. without an oak, the air has to be sucked into the house through small cracks and leaks in the walls, where it mixes with the air that you payed money to heat, and cools it off. now you have to pay to heat it again. and you'll have more cold drafts.
