If the smoke dampers have built-in smoke detectors, a UL listed assembly, I beleive those "smoke detectors" do not have to be connceted to FACP per NFPA.
But if the smoke dampers are also required to be closed, by code, upon detection of smoke in the area served by the smoke dampers or other action such as EPO in a computer room, the controls need to be wired such that such smoke dampers close upon detection of smoke or activation of an EPO in the areas served by the smoke damper. (This in addition to it being able close upon smoke by its own detector)
In practical sense, it is always better to know why a damper closed, and hence it is good to conncet the smoke detector to (or monitor its alaram contact via) the FACP.
You can check with mechanical, but I beleive there smoke dampers available which are listed for use with a 'system' smoke detector. ( I think.....)