No. Dental numbing is local anesthesia, which numbs a small area so you stay awake and do not feel pain there. Surgery may use local anesthesia too, but it can also use regional anesthesia for a larger area, sedation to make you drowsy and relaxed, or general anesthesia to make you unconscious. So dental numbing is one type of anesthesia, not the same as all anesthesia for surgery. Verify the exact plan with your surgical or anesthesia team in case they want something different for you.