Yes. Conger eels are edible fish. The U.S. Food and Drug Administration’s Seafood List recognizes species such as Conger conger (common name sea eel; acceptable market name “Eel, Conger”) and related congers as marketable seafood.
Like many marine fish, some conger species carry FDA-noted species-related hazards, so buy from regulated sources and cook thoroughly (FDA guidance for fish is an internal temperature of 145 °F / 63 °C). Recreational catches may also face local contaminant advisories.