Is it possible for wisdom teeth to be removed using just a local anesthetic ?

Yep: Local anesthetic, if used by a skilled person (and we dentists like to think we're skilled) you can dismantle someone entire face. The best reasons for being asleep is that you won't be worried, it makes it easier for the surgeon to take out your teeth or do other work needed. But, yes you can have your wisdom teeth removed with only local anesthetic.

YES: I do this routinely as it is better for the patients. They can better take care of themselves post surgery. You will hear noise and feel some pressure but that is all. Ice on and off for 72hrs post extraction and use Motrin 800 mg 3x/day for three days, sleep at a 45 degree angle and follow all other PO instructions.

Yes. : A lot of dentists use local anesthesia without any sedation. The benefit of the local is that it also gives you post op pain relief.

Sure: But it may not be completely comfortable for you. Most people choose to go to sleep. If you use just local anesthesia, you can expect to feel a lot of pressure and vibrations from the drill, if they have to use it.