What physically happens when a person does not lift their hands over their head at all? Sleep, drive, work, home, will the nerves atrophy?

Unlikely. If you are not physically active or your physical mobilty is limited, you could develop loss of your muscle mass, or muscle atrophy, over a long period of time. But it is unlikely that you will have atrophy of the nerves unless there is some sort of nerve injury.
Not lifting arms. The nerves generally do not atrophy but the innervated muscles will. Also you may develop dependent edema (swelling).