Not more or less than someone who verbalizes their thoughts more. I would think it is orthogonal to inner voice. Do you think otherwise?
I think people with an inner voice don't notice their 'random' memories as much because they don't fit the narrative. Like confirmation bias, the bits that don't fit get filtered out, yet visual narratives are more flexible than that.
When you dream, it's like a montage, right? Do you hear sound at all? The dream still makes sense when you're in it though. How is waking reality any different in that regard?