If you can't shoot and scoot with any weapon you are not effective. So yes, it isn't just possible, it is a must. In the MoH beta snipers were always easy targets for anyone because they NEVER MOVED. Luckily, the maps were balanced that they could easily be taken out from flanks, or even head on. In MW2, snipers had lanes that allowed them to sit and take out anything that moved, giving the opposing team difficulties in taking them out, unless they used a noob tube, which then led to noob tube wars, which ruined the game.
My theory on snipers: Shoot at me once, I know your general location. Shoot at me a second time, I know where you are. I can see your tracers. If you don't hit me at this point, I am going to kill you, and you have 2 options: stay where you are and die, or move, and possibly die. Also by this point, I have told my friends exactly where you are, and even if you kill me, you are going to have a hailstorm of bullets coming at you.
I do not find sniping in any shooter a reasonable or even respectable form of playing at this point. The sniper rifles are some of the easiest weapons to use and exploit. They usually camp, and they are almost always selfish people who just want to run up their kill count, let alone win. If the sniper is playing WITH the team, calling targets, and giving support, then they are doing their job. Few people do this.