Can a torn rotator cuff muscle result in aching in the shoulder and arm without any real restrictions in movement?

Not likely: A torn rotator cuff can definitely cause pain in the shoulder and arm, but the vast majority of the time the pain will be worse with motions like lifting your head over your arm or reaching behind your back. If you have absolutely no increased pain when you move your arm, it does bring the diagnosis into question. A pinched nerve in the neck can cause shoulder that is not worse with motion.