I suppose it’s possible. The Mongols made two attempts on Japan, both driven off by tyhoons, and some of the damaged ships could have drifted a long way.
But Mesa Verde is a loonng way from the coast and it’s hard to see why they’d hike all that way to attack people who just didn’t have that much to steal.
Also, nobody’s ever found any evidence of metals, recurved bows or other technologies the Mongols were perfectly familiar with.
Archaeological evidence has come out in the past few years to indicate that the cannibalism and violent deaths could be sourced from what is now Mexico. I have sources at home. Can’t get to them now.