No. FC was TNG movie, and having Sisko there would have taken away from the TNG cast.
No, it wouldn't take anything away from the Next Generation cast. If he had been in the movie only as long as that nameless helmsman it would have been fine. What didn't make sense was having Worf be the only recognizable person on Defiant's bridge. It doesn't ring true that Sisko would send the Defiant out to fight the Borg while he stays home whipping up some jumbalaya.