It's kind of a tricky question. I consider deafness to be covered under the Americans with Disabilities Act. I want my Closed Captions on TVs, I think HDMI cables should transmit CCs (BIG issue right now), I want to see more CC options for movies and other public entertainment. I'd like to see better communication for the deaf and HoH when it comes to announcements on public transportation, including busses, subways, trains, and planes. So in that sense, yes, it's a disability that should be covered by ADA and public accommodations should be made for it.
But do I personally consider myself disabled? Well, I'm "not able" to hear perfectly, so by definition, yes, but emotionally, no, not really. It feels like more of an inconvenience than a disability. I can walk, move my arms and legs, exercise, drive a car, use public transportation with no problem, move through life as I wish. I can see, read, think, feel (emotionally and physically).
I had a long and fruitful career for 25 years after my hearing loss started.
That said, if my hearing had been as bad 30 years ago as it is now, I probably could not have had that particular career. I don't know what else I would have done, as my career suited me perfectly in many ways. I suppose I would have done something similar but less demanding in terms of learning new languages.
I don't collect SDDI, but do have a pension from my gov't work.
I would not judge someone negatively, necessarily, for collecting SDDI if they were totally deaf and could not find a job. There's no denying that it is not easy. That said, obviously there are deaf people who are perfectly capable of supporting themselves and do so.
It's a complex question that is not easily answered "yes" or "no."