I think one of the problems with discussions of guns within any topic is that the US is not a good example as, for whatever reason, it behaves vehemently different than many other first world countries. Perhaps the best approach is to compare different western European countries where laws are different (i.e. Switzerland little gun control, Germany armed police and tight gun control, UK unarmed police total gun ban, etc.).
As for testing whether being armed changes someone's behaviour, wouldn't it perhaps be possible in a totally controlled environment, of course I have little knowledge of psychological research, but as far as I understand there are studies that do similar things, though I don't know whether they are valid. I saw something on a BBC documentary once where they tested whether temperature influences a person's behaviour. They gave the applicants either a cold drink or a warm to hold and then asked (after a while) a question, which apparently was answered differently depending on what the person had in their hand.
Of course I also know that a vast amount of published studies, especially in medicine, are total bullshit (makes sense to if you are basically forced to publish to advance in your studies), but I'd be interested to know what inimalist thinks of a study like that and whether something similar with guns would not be possible?