It may be of little quidance to the OP, but here is my recent experience on "late check in" for bags with SQ at SIN.

I had done OLCI but arrived very late at SIN (20 min before dep. and entirely my own fault) - obviously it was too late for bagage drop but the agent printed my BP and suggested I ran to the gate (obviously the gate was a far away as possible; F60 at T2) and SQ would accept the bag on a later flight. I made to the gate 10 min before dep. and was the last pax to board + the bag arrived on the same flight the following day; it was labelled with a special/late check-in label. Pretty well done by SQ I would say.

Whether SK will do the same, I have no idea, but I suppose if you have done OLCI and you print bagage tags from the check-in kiosk, I think you can always blame confusion, queue, lack of sign for bagage drop whatever, for being a few minutes late at the bagage drop counter (there is no way you can drop the bags on the conveyor belt on your own)

Anyway, to my knowledge there is no practise/rule that SK will rebook you for free if you are deemed to have missed the deadline check-in. If you are late for check-in = you are on your own = you need to buy a new ticket if you would like to fly.