Is there a link between severe cervical spondylitis with cough when lying dow?

Possibly: If the esophagus is distorted by the spondylitis, there may be misdirection of saliva, mucus or other fluids into the trachea, known as aspiration, resulting in cough.

There can be in : Terms of what is known as valsalva maneuver. Severe degenenerative changes or spondylosis can lead to narrowed spinal canal termed spinal stenosis & when you cough, sneeze or bear down the spinal fluid within the dural or nerve sac expands within the canal temporarily due to a backup caused by this action that can cause pain. Also the motion of the head & neck moving can cause pain with this.