Not quite. Should a single man with a single province with no army to speak of be destroyed, the Mongols would not simply go elsewhere. They would send another wave. And Subutai's army wasn't the only one inflicting damages to the surrounding powers.
There were multiple waves happening only decades apart in Persia as well as in Russia. Being defeated by one litle Duchy doesn't mean the Mongols stop... it means they will continue relentlessly in the next few decades. While Russia was being attacked, so was Anatolia. You don't stop the Mongols by defeating a small province. It's just silly. Even the people who defeated the Mongols, accepted Mongolian Sovereignty.
I dont doubt the power of the Mongols in history but when they went over whole Europe to England in all of my games like in CK 1 its a total gamebreaker. They even built the best forts in every province, those nomads ;-)
I think we have to find a more gamebalancing solution , because i wanna play the game for fun not having to build a Europe spanning Superpower to be able to destroy the Mongols as soon as they arrive or its game over. I also think the EU horde system might give a good basis. I also tried to "cheat rather historically" by making them a normal Hungarian nation as sson as they reached middle Europe, but they are already too strong then, i would like though if they could settle somehow in certain circumstances and end the horde rage. Until then i guess they should be out for gold more than land, and the more contact they get with western europe the more they should settle down maybe and become a "normal" nation.