Once you've made the decision, born of mental illness or personal rage, to shoot up a place, I don't think the presence, or absence, of any gun law, one way or another, is going to dissuade you. And, spree shootings are nothing new, they even happened back in the 50's before gun control was even a thing... the idea that arming the entire populace of a town or the entire facility of a public institution would dissuade a crazy person from shooting it up is a fantasy.
They may go for "safer" targets, I can't deny that, that they may deliberately start with an area they know is enforced gun-free, but, the ABSENCE of any gun free zone will NOT deter them from just walking out the door and opening fire. They simply go where there are likely to be masses of people not prepared to fight back, malls, schools, churches, they're linked by easy public access to LOTS of potential casualties, that's what makes them appealing, the fact there isn't likely to be an armed presence of any magnitude (before first-response) is a contributing factor, but not the cause. Eliot Rodger shot up his home town, the fact he didn't start at a school, or a "gun free" mall, or if he chose his starting point based on any gun laws at all, doesn't make anyone he killed any less dead.
The argument over who has final say whether the teacher has a gun in their top desk drawer "just in case" is a pointless exercise in political ideology that angers many and solves nothing. No disrespect to those who have lost loved ones to the actions of a mass shooter, but, you're more likely to be killed by a drunk driver in this country, and nobody seriously proposes arming everyone else on the road with a breathalyzer and allowing them to pull over their fellow citizens for a sobriety check anytime they feel threatened..... somehow, crazy people with guns are seen as morally and ethically worse than irresponsible normal people who end up killing a lot more of their neighbors every year.