My recollection is that I was briefly aware of them working in my mouth but not in any pain.
If your dentist proposes things like this, please, switch to someone else.
(For those unfamiliar, after the shots you feel not much other than some tugging. And you can get up and walk immediately after.)
[1] http://www.medicaldaily.com/baby-girl-cavity-filling-dental-...
[2] http://wgntv.com/2016/02/23/dentists-license-suspended-after...
Without the general I would still have the teeth today.
Still, I don't think the procedure used for wisdom teeth in the US has the same risks as the general anesthesia used in more involved surgeries. It's probably still reasonably described as sedation (in my story, I'm obviously still conscious, just not very aware. I didn't include it above, but I actually asked How much longer? and they just told me to go back to sleep).
Human bodies are not even vaguely consistent in their response to medications.
When I had my appendix removed when I was about 12 I awoke and tried to sit up in the middle of the operation. I remembered it and confirmed it with the doc in post-op. The OP's story of waking up during the wisdom tooth extraction reminded me of my experience. Years later I learned of the connection between pain tolerance and red hair, which I have.