The Mongols continued to be a largely nomadic and warlike people. Just because they conquered a dynasty and took control over it's government doesn't mean that they all just settled down into the Chinese way of life, it was quite the opposite. They continued expansionist wars (Southern China, Japan, Vietnam, Java, Burma, etc.) largely without success. While Kublai attempted to rule as a traditional sedentary emperor, his people continued doing what they had for much of recorded history; they didn't intermarry, adopt customs of, or even interact much with the conquered Han. After Kublai died there were 8 emperors within something like a 30 year period and they were then supplanted by rebellion. So the Mongols becoming "civilized" lasted a whopping 70 years or so (if you ignore the continued war-like behavior).
And how did that work out for the Romans? If I remember correctly, the Ostrogoths, Visigoths, Vandals, and numerous others were all, at one time, foederati of the Roman Empire. Employ the barbarians, lose control, be conquered by barbarians in the twilight of your civilization.
As for the Andals, there is a difference between a displaced, migratory, people and nomadic ones. The Andals were a sedentary group whom fled the expansion of Valyria and brought writing, iron working, and the Faith of the Seven. Fleeing a foe and simply being a wandering horde are vastly different enterprises. If we're drawing parallels, the Dothraki are more like the Huns -- nomadic, disinterested in ruling lands they conquer, driven and sustained by looting, and so on -- while the Andals more closely resemble Germanic peoples whom were displaced by greater powers and were more or less content with settling in new areas after they subdued the local populous.
Seriously, just look at what the nomadic Huns and Mongols (Dothraki) ended up doing after their expansionist era compared to the migratory Germanic (Andal) tribes. They aren't the same outcomes because the initial purpose or cause of their displacements weren't the same.
