So, typically, if people decide to rob a store and see a cop in there, in your experience they don't decide to rob a different store or simply wait until the cop leaves, they just go in there guns blazin?
That seems a bit far-fetched to me. I'm going to guess that your average thief also would prefer not to die if given the choice. They are obviously a little more reckless, given that they've chosen a life of crime and all, but I'd still bet that seeing you with your gun would deter them more than it'd encourage them.
But, consider that there's a bunch of no do gooders who are Not exactly sane, and imho would have no qualms about shooting first. Why do criminals that rob a 7-11 go in and kill the cashier for no good reason, not that it happens all the time, but it has happened, why kill an unarmed person if you have some sort of disguise on...? You risk being charged with murder instead of armed robbery.