Not completely for a mild trauma in a developing human, but depending on how severe the damage is, breaking your neck can be fatal because it can seriously damage the brainstem which is required for life. This part of the nervous system also connects your brain with everything else in your body (i.e. all the nerves the control your other organs and muscles) so if this is damaged those organs cannot manage on their own. If parts of the brainstem are still intact it might be possible to keep someone alive on a ‘life support’ machine that does pretty much everything for you e.g. breathing. Such a person would be paralysed from the neck down and much of growth of limbs etc depends on using them – so if this happened early in life, growth would definitely be affected.