These "sharpshooter battalions" of 3 to 6 companies were units, which were especially adapt at skirmish duty, which was most closely akin to "indian" warfare of skillfully moving from cover to cover. As the war evolved the napolianic tactics of Shoulder-to-shoulder battleline formations proved to be too costly for both sides and it was found that most battles were general fought along the skirmish lines until an actual charge, or advance, was ordered.
Was Marksmanship involved in these "Sharpshooter battalions"? Certainly. But "Sniping" Union General was NOT their primary function. If one popped up in front of their sights they would certainly take a shot at him. But their primary duty was to keep the opposing force at bay.
For example General John Reynolds was supposedly shot by a "Sniper" durng the battle of Gettysburg. He was hit in the neck. Was the sniper aiming for General Reynolds Head, or his Chest? In either case the impact was way off for either aiming point. Certainly no shooter with a CW era weapon would intentionally aim for the neck. The shooter is called a sniper in that case simple because General Reynold was killed. Personally, I believe that it was just some "Johnnie" who simply got lucky and a myth grows up around that. I believe that there were several who, after the battle, claimed to have fired the shot that killed General Reynolds. Certainly the bullet that killed him wasn't the first that whizzed by him that day.
Keep in mind that a well care for standard Sharps, Enfield, or Springfield rifled musket of the time was fairly accurate on a man sized target to 300 or 400 yards (1/4 mile) in any compentant shooters hands. Southerners were known to be particularly good "Squirrel Hunters". That is what made the CW so deadly in the first place. There are many accounts of the enemy fire on both side being particularly accurate and dangerous at 200 yards. You wonder how anyone survived charges to within 50 yards of either armys Battleline let alone any closer. The problem was not in the range of the target, but in seeing that far throught the smoke and movement of the Battlefield environment.
There were, however, specific select men in most commands that were, on both sides, specially issued the long range rifles like the Whitworth, Kerr, and Sharps Rifles mounted with telescopic sights. But they were not that many. I believe that Longstreet had only about 20 men armed with these rifles in his entire Corp. And certainly not 3 to 6 companies to each brigade. It was these men who were employed against specific targets as the Officers and were used much like artillery against particularly difficult targets. Sniping, as we understand it today, was then a uniquely American method of warfare starting with the Revolution and the Longrifle. But it was not a protracted widespread practise of using large numbers of marksman.