I look at it the other way if you can show proof you have a connecting ticket they would let you board but I guess it would depend on that agent if they are a stickler or not. I feel like the issue you could run into is if you are able to check in online for the second flight or if they require you to do it at the airport check in counter to collect your boarding pass and do verification(I’ve had it go both ways but don’t find out until check in opens and I try to do it on the app and it says no) and if so that would be a problem as you would have to go into Korea and baggage would probably also be a problem regardless of carriers alliance as your not on a proper connecting ticket so they just need to get your stuff to Korea not onto a separate flight that’s not in the same booking(carry on is prob best way to go with this situation)