My experience with OZ at ICN is that if they're there then they'll check you in for an OZ flight. I got in to ICN about 0830 (Ship got in well ahead of schedule) and had no problem checking in for OZ 204 leaving at 2040 to LAX. They offered to put me on OZ 202 at 1440 but I had decided to check out a couple of places in Seoul I hadn't been to before. Went into the lounge and had something to eat, got the pass from OZ to Immigration to head back into town with the usual warning to be back at least 2 hours before my flight left. Made it back by 1700 with no problems hit the shower and all was well.
Reason I didn't get a day room was company policy to only get us a room for either an overnight or 18+ hours. (straight ship to airport)