is there a speed that can be achieved when at this speed one's neck actually breaks?

The sudden acceleration that happens when someone rearends you often causes whiplash-damages...In the most serious instances the neck might actually break (allthough not enough to actually sever the spinal nerves)

Going with zitizenGkar's suggestion, it's more likely that "breakneck speed" would refer to the speed at which hitting something would likely break your neck. The exact speed would vary depending on the vehicle.