So if there is a Coptic Orthodox Church, is there a Coptic Catholic Church (rite)? Excluding modern missionary activity??
Whether they are original-Catholics, original-Orthodox, Oriental Orthodox ("Miaphysite") ("Non-Chalcedonian"), or something else, depends on whether you think the Egyptian Churches were Catholic or Orthodox (or what?) from the git-go.
I personally would say Catholic-Orthodox, with a couple of translation glitches. "One Lord, one Faith, one Baptism" --- so I always hope for the best.