From what I remember, Romans were failing hard while fighting with Parthian hit - and - run cavalry tactics.
Also, Roman Empire despite common belief didn't rely on
winning almost every battle but
winning almost every war, what I mean: Romans regularly experienced apocalyptic defeats
- obviously Hannibal
- Pyrrhus
- Boudicca
- Germanic Tribes
- Dacia
- Parthia
- Huns
etc.
But they relied on insane ability to regroup, learn from their own mistakes and slowly methodically win with enemy because of superior training and resources.
The problem is, the Mongols would be IMHO too fast to be defeated that way. Come on, these guys managed to conquer everything from Southern China to Persia and Hungary during few decades. If suddenly Mongol Horde appeared in eastern part of Roman Empire I am pretty sure they would annihilate Roman Legions and not give Rome enough time to counter attack... IRL Mongols annihilated modern Iraq and the only thing which stopped them from reaching Mediterranean Sea was Mamluk victory. And Mamluks won because of their superior light cavalry. Rome was relying on massive infantry forces, like China...
Generally the only armies which defeated Mongols were:
- Mamluks: because of light cavalry
- Indians: because of cavalry
- Vietnam: because of superior defensive tradition, strategy terrain
- Japan and Java, because of naval fails of Kubilai
Rome had none of these. It struggled with Parthia - Mongolia would massacre at least eastern parts of Empire.