not as much as you may think.
probably the best way to find out is to look into your graduating classes and see if anyone went for nsg, and how many got it.
a tremendous board score from a no-name allopathic school compared to just average from yale, and theyll take the no-name in a heart-beat. esp if he's got research and great reccs.
one thing that may help tho is if you have a home-program in nsg. this allows you to research in the field of neurosurgery, and perhaps contact those outside it. furthermore, your reccs would come from names that the interviewer may recognize
but even if the school doesn't have a neurosurgery program, do well on your boards, research, get good reccs, and do well in your clinicals and you should be okay. however, if it's an osteopathic school, its a much different story.