Do people with cervical spine stenosis have a lot of pain?

Usually not. Cervical stenosis can cause pressure on the spinal cord which can cause weakness in the arms and or legs. People often complain of fine hand movements like buttoning and dropping cups/glasses.
Maybe. Cervical stenosis (narrowing around the nerves or spinal cord) is common and may or may not cause pain. If a nerve is being pinched from the stenosis there may be pain or tingling in neck, shoulder, arm or hand. Sometimes people have weakness or numbness but no pain. As always, see a doctor if concerned.