The problem with the huge whole house fan is that it can depressurize a house which can cause a naturally drafted combustion appliance to backdraft into the house. The flue gas of a typical gas furnace (or boiler or water heater) contains some CO, typically less than 25 PPM, which would then be diluted with air, if it backdrafted. It takes hundreds of PPM of CO to kill you, depending on concentration and how long exposed.
If your furnace is a natural draft furnace (relies on hot air rising and goes up a chimney), an exhaust fan in your wood shop would probably not affect the draft. If your furnace is sealed combustion (takes its combustion air from outside and exhausts through the wall), then it will definitely not affect the furnace.
FYI, at best, a CO alarm will never alarm at a level below about 35 PPM, and a digital one will never indicate a level below about 25 PPM (it will show a zero for levels below 25). Only a more expensive (>>$100) calibrated CO detector will show levels starting at 1 PPM. Prolonged exposure to low levels of CO can make you feel tired.