If you're flying on one ticket then you should be able to check through (though thinking, I'm not 100% sure how things work from a customs perspective so even then the answer might be no or that you would have to reclaim bags - but at least you would have the protection a single ticket affords). If you're on seperate tickets then you won't be able to check through at all and it's difficult to see how you'll manage - an overnight in CPH would seem likely.