Interestingly, you're probably awake for more than 3 seconds but experience propofol-amnesia. At least, I did: I spoke with my surgeon in post-op (and said embarrassing things) and he shared with me some other embarrassing things I'd said after I "blacked out" (count back from 10).
The amnesia was considered a benefit because it's not the case that you want to remember everything that happens immediately before surgery...