Oh no…not in the extremis!!!!
Well, for one thing, your assumptions are that there is one guard for the whole school. Secondly, you assume that she or he is in a softened position with no intel about what may happen. While it is true that attacks can come from anywhere at any time without warning, there is often some sort of indication; a threat made, a look that is given etc… Retail store security guards can usually spot someone who is pinching merchandise. Thirdly, the shot itself if they do shoot the security guard first will give the rest of the school some sort of warning that there is an intruder on the campus. Now if the shot is fatal, that is one thing although it will still act as a warning. If the guard is able to push a panic button or some similar device, the authorities have that much more of a jump on the situation, they can lock down the school, etc…
I will be the first to say that it is a bad idea. It is the quintessential reasonable response to an unreasonable situation.
The bottom line is that whatever scenario you want to enlist, police involvement will be on the menu. Now why do you call the police? To take care of the shooter. Having someone there who can take care of the shooter at the outset just makes sense. Using your logic…”The killer will be able to recognize the cops and they’ll be shot!!! Really?
Almost all mass shooters plan the shooting to at least some extent (that I have read about).
They will shoot the guard first. The guard will have no warning. The nut will simply walk up to the guard with a concealed weapon, pull it out and shoot him before the guard has time to act.
And what can the guard do? Shoot a kid because he suspects he might be carrying? No chance.
The guard cannot shoot until he sees a gun. And by then, it's too late.
And what warning to the others? All of the high body count murders had to have an opening shot. I am quite sure others heard it. Yet they all had high body counts.
So that throws the 'warning' scenario out the window.
And besides, your idea would cost tens of billions of dollars (assuming you use multiple guards per school)...that is ridiculous.
I hate to admit it - but Trump was right. Just pay teachers a little extra to carry concealed weapons (but they have to remain concealed or it's pointless).
There is no way a whacko who craves a high body count will start shooting up a school if he has no idea how many teachers are carrying.
And if students/parents don't like armed teachers? Tough.
It's better then their kids getting blown away.