Humans very easily process language. If they know a language, I think they'll have some sort of 'internal monologue'. Also, pop culture promotes a conscience in that sense. So, I think anyone who's fluent with a language would probably talk to themselves, and that's what a bunch of their 'conscience' would look like.

But for humans without language, we still have brain areas for processing pleasure, danger, 'gut feelings'. Like humans with language, their behaviour/conscience would probably be shaped by what's worked and what not worked in the past, as well as survival instincts. But it'd be more emotional or physical than talking to oneself. That's my two cents anyway!