A more period appropriate analogy would be the Norman invasion of Ireland in 1169. The King of Leinster was getting soundly beaten by a rival Kingdom. Instead of submitting to his enemy, he fled to England and then France to submit to the King of England/Duke fo Normandy. He came back with English troops and the King of England assumed Overlordship first over Leinster, then over all of Ireland.
Another example is the region of Septimania (today southwestern France, around Narbonne). Until the 8th century it was part of Visigothic Hispania. When moors invaded Hispania they pushed up to Narbonne and Carcassone. Seeing that Spain was lost, rather than fight only on their own the local Lords decided to swear allegiance to the French King, leading eventually to the battles of the Song of Roland.
A third example is the integration of Bohemia in the HRE. Bohemia was a first only the holdings of a powerful vassal Lord of the Kingdom of Moravia. When Moravia found itself threatened by Mongol invasions, Bohemia jumped ship and swore allegiance to the emperor on his western frontier. Moravia was soon after wiped out by the Mongols.
A trend worthy of noting there is that every single example was a Lord. Not one single Monarch willingly submitted himself to another. Lords can jump ship whenever, for whatever reason. Where the illegal realm merger rule comes into play is when two rulers decide to peacefully become one entity.
