That is nearly impossible. Your neck is used to breath, which you need to do to live, but can live for minutes without breathing. A neck shot would also cause one to bleed out quickly, but again, not in instants. There are a very few people who have survived a neck shot.
Any paramedic who had the time would try to save a neck shot, just on the off chance that he might. In a triage situation, a paramedic might be forced to ignore a neck shot for better patients with better chances, but there was no one else needing care in this situation.