It depends upon the kind of anesthesia.
For conscious sedation type light anesthesia, no
But for knock-you-out operative anesthesia yes. How anesthesia works has been a long time medical mystery. The most recent research gives us the thought that it triggers the portion of your brain that induce sleep hard. Now part of sleep is paralyzing the body, so that should shut down reflexes. Operative anesthesia also slows or stops the internal movements o the body - which is great for the surgeon.
Not sure about other states of unconsciousness..