does your building have a smoke evacuation system? If so, Relay bases on local detectors may not be enough.
If you have a generator I would use a 120V equipment branch circuit.
I have never used a Smoke damper that required power to close. I have seen units that close whenever power is droped. If it is a Fire/Smoke damper it will have a fusible link that will drop the damper. I have always used a Macabe link. This will drop the damper 'independantly' of the fire alarm system. The ones I have used mechanically break the linkage from the motor. Because the ones I use Spring closed(not powered closed) the damper snaps shut, regardless if the fire alarm wiring is intact, or if power is on.