I can not say if yours would be cleaner with a forced draft system. My boiler generates almost no smoke unless i mess up loading it. When the fan is off, there is the tiniest wisp of steam/smoke coming from the chimney and there is zero glow within the stove if i open the door. There is a motorized damper on the air intake that seals completely when the fan is off. When the fan kicks on, the fire is blazing in seconds. I never have to clean the chimney or stove but i do when i am shutting it down in the spring to extend its life. Otherwise, i could easily go 10, 20, or more years without cleaning it. That is not true with other brands that i have experience with (one i owned needed cleaning every week or two).
I do know all of the stoves that i see on the way to work belching black smoke just have a motorized damper to control their burn.
Ken