Yes an arrow will kill a deer with a neck shot. Worked in an archery shop for a few years and have seen the results. IF the broad head hits just in the right spot it can sever the spinal cord, instant collapse. IF you hit the arteries or veins it will hemorrhage just like any other vital area. It is a low percentage shot that should be avoided unless there is no other choice on an animal that is already wounded. I have also seen several examples of broad heads stuck in vertebrae, from high shots above the lungs, that were recovered after the deer was taken later by another hunter.
I would not recommend a neck shot as an ethical choice for archery, we don't need the negative results or publicity.