Would I be asleep while having oral surgery on my teeth?

Can be. Many people choose to have conscious sedation or even general anesthesia for this. Sedation (I.V.) is safer and perfectly adequate. Good Luck.
Of course. Thanks to sedation dentistry you can have a number of dental procedures or surgery performed in just one visit. Ask your dentist for more details and request IV sedation.
Most likely. Nearly all oral surgery can be done with just local anesthesia but a large number of people desire to not be aware of it because it may entail cutting of the gums and teeth. Also many are nervous about having oral surgery and desire anesthesia. If the procedure is very difficult, long or possibly difficult to numb adequately anesthesia is appropriate. Talk to your oral ; maxillofacial surgeon.

Related Questions

Can you please tell me if I will be asleep while having oral surgery on my teeth?

Oral surgery. Not necessarily. You may opt for it at an oral surgeon or get just local anesthesia. Its your choice usually.
Not necessarily! . Most dental procedures are in reality "surgical" and are done without being "put to sleep" with general, twilight or oral sedation. Root canals, gum treatments, extractions and fillings all are successfully performed under locally injected anesthetic with less risk to the health of the patient and at less expense. Exceptions: severe patient anxiety and/or need for immobilization.
If you want to. Most dental surgeries can be done with local anesthetic. Many people would rather not be awake for these surgeries and ask to be sedated. Many oral surgeons prefer to perform these surgeries under sedation. Ask your surgeon the pros and cons of sedation.
Optional. You need to discuss your options with your oral surgeon. Many people opt for conscious sedation or general anesthesia. Sedation is safer and all most people need. Some few opt for just local anesthesia and are fully awake. The choice is yours if you are medically cleared for sedation. Best of luck.