From reading their website (in English, I suppose the Korean one probably has better info though but I can't read Korean) it doesn't seem like I can do on-line check if it isn't domestic.

I don't recall ICN transit that well but I know for other airports in Japan you cannot transit without a BP.

Yea for ICN 2 hours may be a bit tight, given immigration seems very slow and backed up sometimes.

I ended up not booking it. Thanks