Will antibiotics effectively treat anthrax infection?

Anthrax. It depends which kind is involved. Inhalation anthrax is very serious, and only 25% respond to antibiotics. Cutaneous and gastrointestinal anthrax responds much better to antibiotics - better than 50 - 60%.
Not guaranteed . Antibiotics are not 100% in getting rid of infections including anthrax. When the disease course is late or fulminant, it becomes harder to treat. For example sepsis.