When the dentist put me under local anesthesia to have my wisdom teeth out, I'm told I was awake and responsive during the entire procedure, but I can't remember anything from the time I sat down in that chair until I was in the car on the way home.
This is, I'm told, a sign that the anesthesiologist did his job well. They're supposed to keep you below the memory threshold.
What this tells me is that there is such a threshold. If you're tired enough, you can technically be awake but be recording very little in the way of long-term memories.
I read the police report of my bicycle accident which occurred about 3 weeks ago. The officer wrote that I was awake and responsive during the transfer from the ground to the ambulance. However I don't remember anything from moments before the crash to when I was already being moved to the emergency room from the ambulance. It's a good 20 to 25 minutes that I have no recollection of anything. When I saw myself being carted into the emergency room all i remember was riding along the road at about 33 MPH (displayed on my bicycle computer).