Do Cataphracts give Byzantines an advantage over Mesoamerican opponents?

Cataphracts take reduced anti cavalry damage, so Mesoamerican pikemen won't hurt them. If they go for archers, Byzantines can go skirmishers or Light Cavalry line. The Cataphract's bonus damage against infantry will crush mesoamerican native units. Cataphracts do lose against Heavy Cavalry line, but Mesoamericans don't get the stable so no fear of that.

Is my theory sound?