I don't think that's very likely, but at the same time it isn't impossible. At one point in the technological advancement the virtual reality might be so realistic that we can't seperate the real world from the simulated one, and if enough senses are engaged during the simulation it wouldn't be unlikely that we would be experiencing similiar mental situations as those who've actually been in war.
I'm pretty sure it depends on wheter the shooter would be realistic or arcade'ish, and the fact if we should be able to feel physical pain or not during the simulation.
One thing I can already forsee with this kind of technology is an increase in deaths related to gaming. If a person believes something is real enough it can get their heart racing. That heart rate stays at or goes over 180 beats a minute for a long period of time you're looking at cardiac arrest. Can also have the possibility of a cerebral neural overload of sorts taking in too much information.
However, it would be pretty dang cool to have a new level of immersion for gaming. Sadly I can already see the military brass salivating at the thought of this putting their guys into a matrix world to train. All it costs them is power to run the machine since every bullet fired, every missile launched, and every death is all an illusion.