Ever since paintball was first played people have used it as a way to simulate warfare and tactics. Following 9/11, people were even convicted of conspiracy to levy war who had used, as part of their training, paintball. While paintball in general and woodsball specifically do resemble warfare, how much does paintball help someone prepare for actual battle? There is no single answer, but I would suggest that it helps very little for a number of reasons including objectives, equipment and required skills.
The biggest difference between paintball and actual military combat is that paintball is a finite game with limited objectives. While there are large scenario games of paintball, my experience is that these are, for the most part, just collections of smaller games being played simultaneously (even if they are coordinated). Paintball has objectives such as eliminating the opposing team, collecting flags, holding outposts, finding hidden treasures and other, ultimately meaningless objectives on a finite playing field in a limited amount of time. Wars cover huge areas with countless objectives and often last for years. In paintball the goal is to engage the opposing side, while in war you generally seek to minimize conflict.
But, some might say, in war you do end up in situations that resemble paintball situations and your paintball skills can transfer to the battle field. That brings up the issue of equipment. In paintball you have limited range and limited options of what you can play with. Paintball guns all shoot approximately the same speed and distance and have limited accuracy. Beyond the basic paintball gun, the equipment such as rocket launchers, mines and grenades is gimmicky, inaccurate and inconsistent. In real war you have firearms, demolitions, air support and armored vehicles which paintball does not teach you to use or to play against. Learning to walk the trigger and shoot 15 balls per second is cool, but that doesn't prepare a player to deal with tanks and airplanes.
But, some might still argue, you may end up in the woods with just small arms during the course of a battle. The difference that will really come into play at this point is skills that paintball players learn. Because of the short range of paintball equipment, most paintball players are within 40-50 feet of each other when one or the other is eliminated and the entire focus of the game is in a limited area. In real conflicts, you rarely get within several hundred yards of the enemy before fire is exchanged. All the quick sprints, runs and stalking that paintball players rely on are rendered mute when someone is shooting a real gun at 4,000 feet per second (compared to a paintball gun shooting approximately 300 fps). Plus, the entire concept of hiding behind bunkers is almost useless as modern weapons have no issue with going directly through trees, brush and most of the bunkers used by paintball players. The skills just don't transfer to the actual battlefield.
I have never been in the military, so I can't say that paintball won't help people become better soldiers, but, I do have a lot of experience with people coming from the military to play paintball and the skills don't transfer very well. Overall I would say that military players who first play paintball are no better than any other beginning player. They may be able to hit a quarter at 300 yards on the firing range, but that doesn't mean they can hit a player running across the field. They typically don't know how to hide in the woods very well and they definitely don't come in with an understanding of small field engagement. Some military players get pretty good at paintball, but that's from playing paintball, not from their military training. Lots of military players do play paintball, and that's because it's a lot of fun, not because it helps them prepare for war.
While I can't guarantee that paintball skills won't make you a better soldier, if you really want to go to war, I'd suggest boot camp.