Mmm, not really. The First Crusade was lead by senior nobility not royalty and was a response to a call by the Pope and the Byzantine Emperor to free the recently conquered Holy Land from infidels. The Byzantines hoped to get easily manipulated westerners to fight for them, but the whole thing took off and became an act of faith, at least in principal. In practice it was a convenient way to ship off surplus warriors to the east to do good deeds and find themselves some treasure.
The First Crusade succeeded in part because the Muslim world itself was divided, The Turks having not long arrived on the scene and disrupted the traditional Middle Eastern power balance, providing the Crusaders with a succession of independent city states to swallow up on the way to Jerusalem.
Subsequent crusades did have royal backing but on an individual basis. Barbarossa led a huge army but didn't even make it to the Holy Land. Most of the time the crusader states were left to themselves to defend what they had with their local forces and a regular trickle of adventurers from the west.
The Fourth Crusade was a special kind of mess, basically a dynastic struggle within the Empire where one party called in a passing Crusade to help, with the inevitable disastrous result. The crusade never made it to Jerusalem, and Byzantium never recovered.
It's a fascinating period, rich with the mix of east and west culture, and medieval and remnant ancient culture.