In The Walking Dead universe, would a sensory impaired person become a sensory impaired zombie, or would their dead/damaged nerves become as functional as a "healthy" zombie's nervous system?
Zombies in The Walking Dead become zombies with whatever wounds they had in life.
They also seem to use their senses to hunt - ones with rotted eyes cannot see, ones with no nose seem to have difficulty smelling.
It's therefore reasonable to assume that if someone was, for example, blind before dying, they would reanimate as a blind zombie.
TWD seems to generally follow the Romero style of zombie, so one can reasonably assume that (like Romero's zombies, as described in The Zombie Survival Guide by Max Brooks) the roamers (and lurkers) use all of their senses equally, instead of being mainly sight-based like living humans.
From the Letter Hacks section of Issue #139:
We were both wondering if someone who was paralyzed (before or after the outbreak) had died and turned, would they be able to walk despite being a paraplegic before they reanimated. (snip)
They would be paralyzed. Zombies are just a nervous system operating a dead body. That nervous system couldn't improve and suddenly send signals to body parts it couldn't when the person was alive.
Based on this word-of-god response, it is safe to say that sensory impaired people would turn into sensory impaired zombies.
According to Robert Kirkman, yes, if a person who is deaf or blind becomes a zombie, they will remain deaf or blind; in the comics, where Kirkman has creative control over the material, this is how it works.
However, in the show (where Kirkman has less control) we did see one situation in which this logic gets turned on its head: in the finale of season 2, Shane kills Randal by breaking his neck. But later, Glenn and Daryl find Randal's zombified body - and it is up and walking around. Why is this a problem? Because if you snap someone's neck, and they somehow survive, they will almost certainly be left paralyzed. So why wasn't zombie-Randal paralyzed? I can only assume that it is a continuity error, and the producers overlooked it.