Given the scenario: Possible? Yes. Desirable? No. If you think you have a reasonable chance of not being raped/tortured/killed if you don’t resist, you’re probably better off not gambling that you can beat him.
Like garygnu’s instructor, we tested this scenario in the dojo to see if it was realistic or not. We were all pretty surprised that if the guy with the gun is simply reacting, you have a very good chance of getting away from the first shot without getting a hole in you. Even if he starts to pull the trigger as you move, if you’re close enough you might either get out of the way or get the gun off line before it fires. Getting shot in the ear is a lot better than getting shot in the head anyway. Before testing we thought the guy with the gun unquestionably had the advantage. On the other hand, Stranger On A Train is absolutely right that you’re not getting away scott free, and you’d damn well be able to follow it up.
Probably several months after we played around with that, we had a guest seminar by an Israeli instructor who worked with the military as an instructor for advanced unarmed (non-firearm) combat. He modified some of the things we’d worked on and pointed out that you’d only do it if you knew you were probably going to get shot anyway. If the guy tells you to turn away or kneel down, and you don’t think he’s going to just take you hostage (i.e.: he’s highly emotional) you’d probably be much better off immediately attacking him since he’s mentally preparing himself to shoot you by dehumanizing you, putting you in a position of inferiority, and in a less advantageous position for defence.
Also, like both Clothahump and Stranger said, less than about 4 paces away and the guy with the gun is being stupid. They show this in movieland for two reasons: 1) It gives the Hero or Heroine a chance to get the better of the situation, 2) Most of the people making movies go for looks over substance. It looks more threatening to have the gun in the guy’s face than to have a more realistic 10-15 foot distance between them. You can cover a 2 meter or more distance in less time than most people’s reaction times with a single lunge. Surprise him enough and you might be able to get another step in, enough to close 3 or even 4 meters if you’re lucky.
This video on YouTube shows some Krav Maga training for dealing with this very scenario. Pay attention to the actual training and ignore the comments from the trainees. Feeling “safer” doesn’t necessarily match reality.