No that’s completely wrong too. The Black Death would have happened anyway because there had been trade E-W along the Silk Road for thousands of years. As well as trade N-S from Black Sea to Baltic Sea along the rivers. Plus by Ghengis Khan’s time, there was sea trade from India and East Asia to ports in the Persian Gulf and Red Sea. Various empires expanding and contracting interrupted trade, but didn’t stop it completely.
The Black Death of the 1340s also was not the first time that disease Yersinia Pestis had been a pandemic in Europe. The Plague of Justinian had happened in the 500s.
So, no you are linking peace with one Empire builder who conquered much of Asia with a plague that already had a history of re-occurring in Eurasia & North Africa for a good two thousand years before. They are not correlated at all. If war had still been going on, the Black Death would still have happened.
In addition, that’s not how Ghengis conquered. He did not invade, take slaves and sod off. He invaded, picked a big rich city, razed it to the ground except for a mountain of severed heads of all the inhabitants- men, women, children. Except for a dozen or so he spared. He then sent these as messengers- submit or suffer the same fate. Most kingdoms submitted and opened their cities gates to him. Until he got to Eastern Europe and they refused.
Now, yes they had slaves, but the purpose of Ghengis’ wars were not to take slaves but to create a vast empire by gaining territory and client kingdoms. You do that by replacing their aristocracy with your own, not by enslaving everyone.