Sure, but the end of Roman slavery was just the collapse of the economy. No one bought slaves any more so slaves became serfs - no longer sellable people but people tied to the land and coerced to work. That's hardly a sign of marvelous progress.
A big hindrance to seeing continuity is that popular knowledge of "romanness" is so focused on the late republican/early imperial era and there is surely not much visibly continuity between early medieval and a snapshot of the Roman state outdated by several hundred years.