Potential shooters need to know that the possibility of opposition exists - from multiple possible sources. That alone will stop many of these attacks.
Yes, the first and best purpose of a screened and trained group of volunteers within the school is deterrence: the shooters who are mostly cowards to begin with will think twice about entering a school with an unknown number of armed opponents.
I don't know about these big city geography teachers, but where I'm from a couple teachers in the Army Reserve have had deployments to the middle east and served their country. They would have done better in this crisis than the cowards out in the parking lot waiting for the perp to run out of bullets.