I assume you mean 'The Mongol Horde'. Historically: led by Kublai Khan the Mongols sent a fleet to invade japan, but their fleet was nearly totally destroyed in a storm, so they never managed to capture japan. (they did create a big empire.. from china/korea all the way to poland/hungary.) All this happened somewere between 1000-1300 roughly.

When you have MI/WE you can indeed play a campaign in which you are the Hojo, you have all of Japan and the mongols land and try to conquer your lands. It's a scenario like 'What if the mongol fleet was not destroyed in a storm - who would've won?' However the mongols don't play any role in the 1530, 1550, 1580 or Sengoku Jidai campaign.