Probably not. ER doctors, surgeons, and physicians cannot practice dentistry, and it is extremely rare to find an ER or urgent care center with an emergency dentist on call. In most cases, a visit to the emergency room or an urgent care center will result in a prescription for some painkillers and/or antibiotics. The emergency room staff will tell you to visit a dentist as soon as possible, and then hand you a bill.
In some extreme (yet very rare) cases, a tooth infection can spread and become a very serious health problem. To avoid an unexpected trip to the ER for a toothache, you should see a dentist once you begin to experience pain. Toothaches almost never disappear on their own, so even if the pain is manageable, you should see the dentist before the problem compounds and becomes more painful and expensive to remedy.
If you have experienced trauma to your face or have not yet taken antibiotics, you may want to consider the ER or an urgent care centers. Antibiotics can reduce the swelling, which may be necessary before a dentist can perform any treatment. But you have been warned – it will not be cheap, and it is not a permanent solution!