It varies. Certainly if I'm just falling asleep, or groggy and waking up, I sometimes get the sense that I was there but not thinking the same way I do when I'm awake.

But that doesn't mean that I'm somewhat conscious all the time. I have sat in class paying close attention to the professor, then felt my friend's hand on my shoulder in an otherwise empty classroom. I didn't notice myself falling asleep or waking up -- time just seemed to stop.