This 1977 medical paper suggests that the neck wound might have been fatal in itself, but through sepsis, since the President's adrenal insufficiency and long-term cortisone treatment might have reduced his resistance to infection if the spinal cord had suffered trauma.
http://jfk.hood.edu/Collection/Weisb.../Item%2001.pdf
It may be that C-6, the sixth cervical vertebra, was partially damaged by the bullet. This would cause a referred shock to the spinal cord, and the President's convulsive elbows-up posture after the bullet strike has been posited as the 'Thorburn position' (from a 19th-century study), indicating spinal trauma.
It's a little speculative. At Parkland, the President was given immediate care little different from what he would receive today -- he was intubated and put on a ventilator, with the tracheotomy making use of the first bullet exit wound -- but the overwhelming problem was the head wound, which resulted in no detectable pulse even though there was 'gasping' respiration for a while. It remains possible that the neck wound would have been survivable.