The problem with volunteering is that it produces inconsistent security at best. You're basically gambling that enough people will volunteer to make a difference, that those volunteers will happen to be in the right place at the right time, and that they'll be effective if they do get to draw their weapons. Between 1998 and 2006, the average hit rate for an NYPD officer firing their gun was 18 percent. Do you think a volunteer with less training and much less experience is going to do better?
It'd be better than nothing, but it wouldn't be significantly better than nothing. If the notion of arming staff is going to be truly effective, you'd need a defense that's both always available and effective... and frankly, I'd rather address the loose regulations and gun-happy culture that enable mass murders than to treat schools like they're perpetually 5 minutes away from a massacre.