Possible - yes, I would think so. Certain - maybe not.

I think it depends on two things -
1. The airport's ability to handle 'overnight' bags
2. The airline's willingness to tag it all the way through for you.

Some airports can certainly handle 'overnight' bags - NRT for example. ICN - I don't know though the comments in this thread would certainly suggest they can. In it, the poster (flying OZ) says "A folder has already been pre-printed with my boarding pass, bag tags (all the way to HKG despite an overnight layover at ICN),..."

The second part is convincing the airline that you're checking in with that it's ok to check the bag all the way through. If you're checking in with AA and you're EXP, then it ought not to be any issue convincing them that it's ok to check the bag through. Show them the itinerary and, if all else fails, assuming it's got some AA legs in it and/or you know the PNR, they can pull it up and see it. The issue for them is probably just whether it's 'ok' to check bags through on to flights that aren't on the itinerary they're checking you in for.

Let us know how it goes - some of us have a vested interest in the answer! I hope you don't find out the hard way that it can't be done but I suspect it's not an issue.

[Edited to add]
You get the feeling from their transfer information that they're pretty organized and the bags shouldn't be an issue. As I was looking at this, the 'light bulb' went on as I realized that any airport that has a transit hotel inside security must be able to handle overnight bags. It really wouldn't make much sense to have a hotel inside security if having to collect your bags was required.