Yes. If you need oral surgery in the Emergency Department, your health insurance will be billed by the Emergency Department. The Emergency Department at a hospital is not likely to be able to treat a dental problem unless it is a health emergency.
It is best to prevent dental problems and avoid costly emergency care by getting routine dental care, both at home and from professionals. Dental insurance plans are available to help offset the costs of routine preventive and diagnostic care, including check-ups and cleanings, fillings, root canals, crowns, bridges and other procedures. There are many insurance companies in the state of New Hampshire that offer dental plans. If your employer does not offer a dental benefit, you can go to https://www.healthcare.gov/ to enroll in a plan.