It is not medically necessary to get any kind of sedation for oral surgery, but in some cases it can make it a lot nicer for you. With local anesthetics alone (shots in your mouth), you should not feel anything the surgeon is doing except for the sensation of pressure. By the way, you probably don't mean "general anesthesia" which is usually done in a hospital by an anesthesiologist and a machine breathes for you. Most likely you are referring to "IV sedation" which is done in the dentist's office, you are semi-conscious but mostly asleep and, the big thing, is you breathe on your own without the help of a machine. BIG difference between the two terms. Unless you are getting something exceptional done in your mouth (and it doesn't sound like you are), the insurance is very unlikely to pay for IV sedation if your policy doesn't cover it.