I’m 100% deaf and live in the Deaf Community— many of my friends were born deaf. They definitely have an inner voice. The fact that American Sign Language does not have a conventionalized written form requires that Deaf people be bilingual in ASL and written English, so most of the inner-voice is in both ASL and English. I was not born deaf, but my inner voice is bilingual as well.
Many concepts can not be articulated in English, but exist in ASL, or can not be concisely expressed in English, but are better expressed in ASL because of its multilayered nature (up to 7 meanings can be expressed simultaneously). I’ve had discussions with my Deaf friends about this and all of them say the same—our inner-voices are bilingual because we switch between the best ways to express or process concepts.
Do we “HEAR” our voices—No. I describe it as having a telapathic feel to it—language and thoughts emerge, but do not process through the mind’s auditory processing channel.