I can't speak for the earlier Crusades, but the ones conducted between the XIII century and the first decades of the XIV century were definetly known. There was a somewhat prolific contact between Europe and the Mongols (Later the Yuan dinasty as well) during that timeframe. There is no greater example other than the distinct possibility of an alliance between the Mongols and the Crusader States against the Mamluks that arised during the XIII century. While said alliance never came into life, it clearly shows that the Mongols realized the nature of the Crusader States, the Crusades themselves and their role in the region.

Source: Peter Jackson, "The Mongols and the West: 1221-1410"