Their morale and organization was 100% when I dropped them off; the battle lasted for a couple of seconds - I didn't even have a chance to look. I'll reload and start the war again to see if their org and morale dropped to 0 during that brief battle, against Korean irregulars. Somehow I doubt it.
It was in 1840. I did it then because I was following the instructions in the Wiki
http://www.paradoxian.org/vicky2wiki/Japan
The Wiki says it's no problem to invade Korea while Japan is uncivilized, and you should do it early because it actually helps you civilize earlier. It's so you can get prestige and so you can already have Korea when Japan civilizes, and the Infamy will have decreased by then so you can go take over another country. My Infamy is 0 and it's a waste of 20 years to have 0 Infamy when I could annex Korea and then 15-20 years later have 0 Infamy again. 15-20 years is a big chunk of the game.
EDIT...
Ok, I did it over and you were probably right, their numbers and morale went down really fast, like from 3000 down to 0 after 3 or 4 days. One of the armies retreated like it was supposed to. Another one got completely destroyed because it had 0 manpower, 0 organization, 0 morale.
I'm using some irregulars and some normal troops. The normal troops don't seem to fight noticeably better than the irregulars.
The Koreans seem to have better military tech than Japan, I don't know which one(s).
So I'm unable to surround them to destroy their stacks since I'm losing half these battles and even when I win, at the current rate, it would take years for some of these to regain their full strength. One went up from 27 to 50-something in a month. It's supposed to be 3000 of course. And I can't buy enough goods to build all the troops I need even though I have plenty of money. Looks like the Wiki was way off.