In a rear end collision if the back of your head encounters a correctly positioned headrest the heads movement is stopped?

Yes. Correct positioning of the headrest may prevent muscle strains in a collision.
Unfortunately, regardless of the position or softness of the headrest, the brain may impact the inside of the skull with enough momentum to cause injury. Also, there can still be issues with the neck and spine, since they move independently of the head when subjected to accelerations.