My great grandmother used to cook right on the edge of the fireplace, in cast iron Dutch ovens. My grandmother cooked on top of a wood stove, and when I was a kid we heated the house with a wood stove in the center of the house.
I cook on a wood stove and heat the house with wood. The only time the stove emits anything into the house is when I light it and the chimney is cold - which doesn't happen that often but can happen if I have not used the thing for more than a day or 2. I built that chimney myself, it is solid brick and does not use vermiculite-insulated liners - i.e. it is built according to the 'old' standards where the chimney itself functions as a heat buffer for the top floor (which is why I built it that way). Given a warm chimney there is more than enough drag to keep combustion products from escaping even when I lift the pan off the fire.
It also helps that the stove and its neighbouring electric companion (which I use as a storage area for pans) is built under a large fume hood which ends in a flue pipe in that same chimney. The warmer the chimney, the more drag in the fume hood. There is no fan and none is needed given a warm chimney.
Of course all this only works if there is enough ventilation into the house since both the stove as well as the fume hood need incoming air to work. This is not a problem in our 17th century farm house, even with all the windows closed there is enough air coming in to keep all fires burning. As long as I keep the chimney and the stoves clean - I sweep it once or twice per year depending on the type of wood I burn - they do their job without fouling up the house.
On the flip side fireplaces uniformly have chimneys (and wood stoves almost always do) in order to get those particulates out of the house. Which doubles as getting the gasses generated out of the house.
I'm not an expert but I'd guess that at least with regards to NO2 that made up for the less clean burning.
If you can smell the smoke, it does not. Wood smoke is incredibly bad for humans. I believe there are some modern wood stoves that seal very well and can prevent combustion products from leaking into the dwelling, but that isn't the case for like 99% of wood fireplaces in the US, at least.
I wonder how those all compare.