Question about general anesthesia.

How sure are we that anesthetics actually prevent pain during a medical procedure? Is there a possibility that the drugs simply blank our memory so we don't remember anything?

I recently underwent a colonoscopy in which I was given Propofol as an anesthetic. True to form, they injected the drug into my IV and the next thing I was awake in recovery - I don't remember a thing. Later, reading more about the drug, I found something interesting. Another name for Propofol is "milk of amnesia" for it's memory erasing effects. So what if I was actually awake the whole time and I just don't remember it? Since it was a colonoscopy no big deal, but what about major surgery? Our autonomic nervous system keeps going while we are sedated .. is it possible that our pain receptors also function, and we actually feel pain and can't do anything about it? I know there are cases of patients being awake but paralyzed during the surgery - maybe it's just that in those cases the memory blanking didn't work 100%. Thoughts?