Can a series of antibiotics actually dry up an endodontic infection when there is no pain, under the direction of a dental specialist (I doubt it)?

Cause of infection. The cause of the infection must also be treated... that is usually leakage of the root canal filling material and/or debris still in the canals. This is usually accomplished by endodontically retreating the teeth. Afterwards, there is always a chance that the teeth will need apicoectomies. Antibiotics alone usually will not be enough. Your endodontist will explain further.