I want to preface this by saying that my expertise is in American deaf history, not British deaf history, but as far as I know I'm the only specialist in deaf history in this subreddit - so I will do what I can.

It's also worth noting that "pre-ASL" is a misnomer here. First, the Regency era refers specifically to the UK, so American Sign Language isn't really relevant, as all countries have their own sign language. Additionally, signed languages in both the US and UK date from the 18th century and earlier, so the Regency era is not pre-sign language.

However, deaf education in the UK during the Regency era was dominated by oralists. Thomas Braidwood, an educator from Scotland, moved his school to London in 1783; with the help of his family, it ran until the early Regency period. The Braidwoods used the oral method for education, but students used some signs among themselves (Jane Poole is a notable case), and we know of sign language being used in the Kent area as early as the 16th century. So it is possible that young deaf women used some sign language, but also possible that they were educated orally.

Whether these young women could have married into status, though, is more about their family station than their deafness. In the upper classes, disability was sometimes seen as shameful, and disabled family members were kept at home or institutionalized away from the family, as with George Austen. (Note that George may have been deaf, and Jane Austen herself may have known some sign language, based on her own writings.) In the lower classes, it was more likely for disabled family members to get some education, but just enough that they could work; we know of a number of deaf people from this period who held jobs on farms, as washerwomen, etc.

So, could deaf women have been part of the Pride and Prejudice style culture? It's quite likely, as deaf people had any number of methods of communication, and were integrated into society - when they were allowed to be. See, for example, Princess Louise of Anhault-Dessau - not from the UK, but a good example of a young deaf woman of the period who was part of her community (even if she did marry her uncle). If you want to stick to the UK, Harriet Martineau came of age a few years after the Regency era, but was perfectly well respected and became a renowned sociologist.

Again, my expertise is very much not in the UK, so I'm a bit weak on Regency society. But I hope I've at least given you something to go on, especially the information about deaf education in the UK during this period, and how people with disabilities were and were not integrated into society, based on their family's priorities.