I'm so deaf I can't hear much of anything, even with hearing aids. I never learned American Sign Language. I lip-read terribly. I also have an inner voice. I read at a grade level above hearing peers. I understand puns.
How did that happen?
I learned Cued Speech[1]. It's not mentioned anywhere in this article. It's a system that, summed up in a few words, uses signs for phonemes. Because of this, I could learn English within English. And when I took Spanish classes, I learned Spanish within Spanish.
I also dream in verbal words. Even after I learned ASL, I still dream verbally. The words are always quiet, a bit muffled -- this is how I heard things early in life, with hearing aids (I have a cochlear implant now). Occasionally I see captions, as if it's a TV show.
A last note. In the article it mentions little d and big D deaf; the way I learned it is that little d deaf people are deaf people in general, and big D deaf is the Deaf culture and community.