I'm curious what improvement, if any, is seen from using the fan on the range hood while using the gas stove/oven. Since I heard about this issue, I've been using it every time I use the stove or oven, and it does make a different to the subjective gas smell around the house, but I don't know if it impacts actual NO2 levels.
Assuming it is not a recirculating hood and it’s venting outside, it should help reduce NOx levels. When you’re venting to the outside, you’re creating a negative pressure inside the home which is drawing in fresh air, which in theory will dilute the concentration. Some systems have “make-up air” which blows in fresh air, roughly equal to what is being vented out.
Adding the make-up air system increases the cost by 50% or something (needs a similarly powerful fan and similarly sized duct for air coming in vs. going out), but any powerful vent hood should probably include one (and building codes demand them in many places, though I think this is often overlooked in practice).