If those who want to carry are given some training by the authorities, above them just going to the range and shooting paper a few times a week, then I can't see a problem with it.
Well, apart from when the police arrive and shoot the teacher because he's got a gun...
Or when the teacher (who would not have been expecting to deal with a gunman) aims hastily and shoots the wrong person/misses completely.
It was only a few weeks/couple of months back that someone pulled a gun in a church and a teenager managed to disarm the guy, then got shot when the police arrived a few minutes later because they walked through the door and saw a gun.
The entire fallacy of a "armed citizens shooting attackers" is completely forgetting that the people being attacked will (no matter how well trained) be suffering from some level of initial confusion, and that it tends to take a lot more than a few training sessions to get someone to be good enough to respond fast in an unexpected situation, let alone the hesitation most people will have when it comes to actually opening fire at another human being.
It's one of the reasons the idea that having a gun in your purse/pocket will help in a mugging is so silly, the attacker will typically be expecting resistance and far more prepared than someone who up until a few seconds earlier was going through their normal boring daily life.
And given the level of training common in US police forces when it comes to firearms handling, I can't see the teachers getting much better...
They'd do better putting armour on every internal wall and door in the school, as the current "hide in a room and close the door" is better than nothing but given how common plasterboard type walls are for internal partitions it does nothing to stop someone firing at random, or a shot that misses passing through a wall and hitting someone on the other side of the wall.