No, although this is a common misconception. Your furnace or ducted heat pump doesn’t produce dust any more than a boiler or a ductless system might. What your forced air heater does do, though, is circulate dust, allergens, and other debris throughout your home. That’s not to say you shouldn’t use your heater! It just means that you’ll need the right indoor air quality system(s) in place to combat this—such as a whole-house air purifier.