While I do not have canon to back this up, I believe that there is a critical component to brain recognition of a direct stare between both the basilisk and the victim. This can be borne out by a couple of things:
- Colin Creevy, Mrs. Morris and others viewed the stare through an intervening instrument (Camera, water, etc), and survived (albeit petrified).
- The stare was nullified once the eyes of the basilisk were put out by Fawkes
Being that there would be no recognition on the part of the person suffering the blindness that they were being stared at by, well, anything, I don't believe that the necessary component is there to assume death would follow.
This is also partially corroborated by the way that the mandrakes are approached. When Neville misplaces his earmuffs, the cry of the juvenile mandrakes makes him faint. The rest are fine, so there is no real brain recognition of the sound. Since a deaf person has no brain recognition, I believe they would also be immune. (I have no conjecture on how it would affect a partially deaf person). There is nothing to indicate that a phsyiological blocking of a sense would be less effective than a mechanical blocking of a sense.
A banshee might be a different matter, as it is not only their scream, but their visage that can cause various effects. (Note: The banshee scream being fatal is not in the original Celtic legends of the bann sidhe or baen si from whence come the modern version of the banshee).