When camping along the Appalachian Trail there are some campsites that require fees to stay at those campsites.
However you can usually pitch a tent anywhere along the Appalachian Trail and camp overnight without having to pay any fees.
Just be aware that some parts of the Appalachian Trail do not allow any campfires so you'd have to bring along a propane cooking appliance to cook food or heat up water, coffee etc.
But as long as you move often as in everyday then yes you can camp just about anywhere in the Appalachian Trail.
It can take days to complete the hike through the Appalachian Trail so you will want to camp during the night and start hiking again the next day.