Most kitchen vent hoods do not move enough air or have high enough static pressure capability to significantly depressurize most homes.
Two exceptions:
Very large restaurant-type hoods in the 700 cfm and up range. Also downdraft vented stoves such as Jenn-Air.
Some modern homes are very tightly constructed. It is possible to depressurize them and backdraft combustion appliances fairly easily, especially if the appliances have a convection type rather than a powered exhaust.
You probably have bathroom exhaust fans and a clothes dryer, and possibly other exhausting devices. A fireplace exhausts a great deal of air while in use, a wood stove usually a good deal less. You need to figure whether the home will depressurize if all these devices happen to be in use at the same time.
It is possible to have what is called a blower-door test performed on your home to determine how tight it is. Actually a good idea for anybody, as overly leaky homes are one of the major causes of energy inefficiency. In fairly recent homes a much greater cause than insufficient insulation.
Whoever performs the blower door test should be able to tell you how much ventilation you need for a given range hood exhaust volume. For energy efficiency, if needed, the ventilation air can be brought in thru a heat exchanger wired so that is kicks on when the range hood is on and a damper closes when it is off.
BTW, a major reason not to heat your home by running the gas stove burners is that one of the major combustion gases released is water vapor. Which raises the humidity a bunch and can lead to mold growth and other problems in closets, behind furniture on exterior walls and other cooler parts of the home.