Shelters are placed at logical mileage points 8 and 13 miles apart and always near a water source. Most also have nice places to tent. For example, I recently spent a rainy night in a great spot well protected by overhanging bushes and trees, yet onl;y a few yards from the Big Spring shelter in NC. There were only 2 other hikers in the shelter, I joined them for dinner and thoroughly enjoyed the company before returning to my tarp for the night. I have done this countless times along the AT. You will have no trouble stealth camping along the AT. There are only a few restricted areas. Here are the general rules for the White Mountains of NH: "The general rule is that you can camp anywhere that is 200 feet from a trail or water source, 1/4 mile from any hut, shelter, or established campsite, and is not above treeline."
Recently in NC I came upon two tents, so close to the trail, I could have easily kicked into them while standing on the trail, and their food bag was actually hanging over the trail. Unless an emergency, I found that a stupid place to tent. Animals use the trail at night, and why do you want people walking by so close?