I'm kind of at a loss as to what you are referring to. What do you mean the heating system won't have to run? Aren't you running the fan to cool the room not heat it? When I was trying to run CO2 in my flower cab, I could only turn off the exhaust fan for about 15min before my humidity went through the roof. If you have a dehumidifier that wouldn't be a problem, but you don't want your humidity at 80% a couple of times a day.
That fan couldn't be pulling too many watts. My 747cfm vortex only uses like 250watts. Those blowers usually use less power. So if it is at say 200watts, running 24hrs a day, with electricity costing like 15cents a kwh, you will only be spending like $20 a month. To me, $20 a month is well worth not having to worry about humidity and mold in harvest. And if your electricity is closer to 10cents a kwh, you are only spending $15 a month.