Well the reason why the Romans had such a difficult time conquering Germany was that it lacked states and infrastructure. The Frankish kings had a better time conquering Germany because the previous conditions were met.Wait, what? I thought the Gallic Empire had the border provinces? Are you asking if they could do what a united Roman Empire couldn’t under Augustus?
Also IMO Germany in the 200s kinda reminds me of pre Caesar Gaul. It was brimming with energy and the formation of large tribal confederations was on its way. Thus for these reasons I thought that the Gallic emperors would have a pretty good shot at conquering certain parts of Germany