I can't speak directly to the braille issue, but let me take a shot at an analogy, from the perspective of a musician.
When people begin playing guitar, not only can't they properly "sense" what they are doing, but their fingers get tired and calloused easily. It can be a tough and discouraging time, as strength is building and sensitivity increasing, but the fingers are getting used to the strain and abuse they need to take as the player improves. Many people abandon their efforts during this phase, unless they are very motivated.
However, the fingers DO gain callouses and a "toughness" that makes playing for longer and longer more doable. And despite the "toughening" of the fingers, players also gain a level of nuance and sensitivity that comes, in part, from being BETTER able to sense their instrument through their fingertips.
Braille is obviously quite a different thing; I would suspect that it is at least as difficult to learn, requiring even greater nuance and sensitivity, but that the practitioners are, on the whole, probably more motivated to do well and gain proficiency. I would suspect that, as with a guitar, while a certain amount of "toughness" goes along with the constant practice, a new level of nuance and sensitivity is also attained.
However, as I said, I am NOT your target user, so I will also be interested to learn what sight-impaired people have to say on the subject!