I always thought that tunic was used by McCoy in the lab or when treating patients because the slick fabric would allow easier cleaning of the schmutz (you know - blood, etc.). I never thought it would be used by other areas, but I guess it would. The engineers might want to wear it when they could get oil, transmission fluid, etc. on themselves

).
BTW, I wonder if the actor playing Dr. M'Benga wore the same tunic that Kelley wore. He seemed to be about the same size, and I doubt they'd create a separate tunic for a guest actor.
Doug