Perhaps not quite the answer you're after, but I was deaf as a child, though I was able to hear as a toddler and had therefore been exposed to spoken language before going deaf. I absolutely had inner voices while I was deaf, to a practically debilitating degree. The isolation inherent to deafness caused me to have strong inner dialogues, to develop a full world inside my head. I would often "go away" in my head, to the point that I was completely detached from and unresponsive to the physical world. It's apparently very unsettling to people standing right by you.

My grandfather used to be fascinated by it, he'd say that I'd gone to my secret garden and that it was ok to leave me alone. Even after recovering my hearing years later, I kept this habit (whether it's good or bad is debatable). Over the years I developed a better hang of it and I can now trigger it mostly at will. The level of introspection that came with all this is rather hard to explain, though for all my quirks, I don't regret it one bit.

not sure about deaf-mute people but https://en.wikipedia.org/wiki/Prosopagnosia is an area of interest for people who study philosophy of mind