Short answer is no. Your stove should be sealed and all the gasses go up the flue and chimney. If it does leak it won't just be CO2 but also CO carbon monoxide, which could put you in a very long slee...
Yeah, and it's an old house so it's pulling fresh air in so replace the oxygen that's being consumed by the fire. But it is a weird thought... so maybe I'll get one of those meter things.