Better steel isn't going to save Rome, or even delay the inevitable, as Rome's problems weren't something they could solve with military might; the empire was rotting away from the inside and nobody could (or would) do anything to stop it.
Now, if Roman smiths had learned to make Damascus steel (provided that it's a product of the process, rather than the metal, used) that could have an impact on Post-Roman Europe, North Africa and the Middle East, as anybody with such a smith in their employ would hold an advantage in equipping their armies (to a degree) over opponents who don't have it. Fortunes could be radically altered in some places; if post-Roman Britons, for example, had a bunch of skilled warriors, with Roman legionary discipline and tactics and training and organization and Damascus steel weapons, Britain might have ended up repelling waves of migration for far longer than OTL. That would cause some major ripples in how the history of the world shakes out right there.
Now, if Christian monks wrote down the process (as Christian monks were wont to do on a number of things that had nothing to do with theology but did add to man's knowledge base) that would have been a net positive for future scholars, as it'd be one less mystery to solve and, also, it'd broaden our understanding of just how knowledgeable and resourceful ancient man was.
Damascus steel can't save Rome, but it can shape the post-Roman world, perhaps in profound ways.