I agree with ElectricAl
A paddle fan is moving the air that is already in the room, not suppling fresh air into the room like an air discharge register where with bad SD placement could prevent operation of the SD until it melts.
It is possible, IMO that the fan in some instances will cause faster operation of the SD as the smoke will travel through the space faster even though it is getting diluted at the same time.
I would hesitate to ask a your local fire guy, in this area they are notorious for arbitrary off the cuff rulings.
He may say yes you are right "no fan in rooms with smokes"
