Happened across this just now in a timeline of deaf history:
1850's: John Flournoy, a former pupil of the Connecticut school, proposes to Congress that land be set aside in the western territories for the creation of a deaf state[...].
I was going to say "Hey, that might make a neat alternate history!" But then I did a little further research.
First I discovered, via Google Book Search, a book by John V. Van Cleve and Barry A. Crouch called A Place of Their Own: Creating the Deaf Community in America, which has a several-page section on Flournoy:
No more bizarre individual than John Jacobus Flournoy is to be found in the history of deaf Americans. [...] Flournoy rarely cut his hair or his beard. He wore a rubber raincoat in all seasons, and he rode about on a small donkey. A prolific letter writer, he wrote prose so convoluted and wordy that it is nearly incomprehensible. [....]
[H]e suggested that members of the deaf community who so desired might think about choosing a place to settle in the American West and then move there and assume all governing responsibilities. In December of 1855 he broached this idea with William W. Turner, a hearing man and one of his former teachers at the American School.
Turner pointed out what I see as the biggest flaw in Flournoy's plan: the question of what to do with hearing kids who are born to the deaf parents. I can imagine several answers to that question, any of which might make interesting fiction.
The other flaw Turner suggested, the fact that deaf people might not want to leave their homes to go live elsewhere, is of course also true; but as the history of Liberia demonstrates, sometimes some people are willing to leave their homes to go live with people who are more like them. (I am of course vastly oversimplifying about Liberia. Still, here's another example: many science fiction fans, and a fair number of stories, have expressed the desire for fans or fictional fan standins to form their own separatist community.)
Anyway, the exchange between Flournoy and Turner was published in the American Annals of the Deaf, provoking "a torrent of comment from deaf and hearing people." Discussion appears to me to have proceeded along more or less the usual segregationist-vs-integrationist lines. In the end, "[m]ost recorded reaction to Flournoy's idea was negative," and so perhaps this just isn't a very plausible alternate history. On the other hand, as the book points out, the people involved in the debate were mostly successful and reasonably well-integrated into hearing society.
At any rate, next I found a discussion thread at alldeaf.com about deaf states and towns; for example, it turns out that Martha's Vineyard had an unusually high deaf population at one point, according to a book titled Everyone Here Spoke Sign Language: Hereditary Deafness on Martha's Vineyard. And apparently there's been more-recent discussion of establishing a deaf town, originally to be called Laurent, in South Dakota or Indiana, that would be English/ASL bilingual. And there's a community called Al-Sayyid in Israel with a much higher-than-usual incidence of deafness.
So not only is it not necessarily a good althist idea, there are actual real-life societies in which enough of the locals are deaf to have a big influence on local culture and language.
So instead of suggesting this as a story idea, I'm just tossing it out as an interesting phenomenon.
I suppose while I'm here I should mention the somewhat related song "They Spoke with Their Hands," by Cat F, which grew out of a roleplaying game involving telepaths but used the analogy of a hearing person growing up in a deaf society.