I'm usually quite late at CPH so I have no experience from this scenario in CPH. Checkin opens strictly 2 hours before (and closes 45 minutes before), so desk is only manned between
11.15-12.30
14.50-16.05
18.10-19.25
Technically there shouldn't be a problem with dropping bags at the midday slot even for the evening flight. Now, since this is CPH where 'the inmates are running the asylum', I wouldn't bet on it. It is worth a try, but maybe best to devise a back up plan too. There are lockers at the airport, strangely enough they are located in the parking area (!) P4.