As someone who regularly flies in to CPH on SK from DUB - another non-Schengen city - I can say that we are regularly dumped in both Zones A and C - so passport control will depend on where you are dumped.

The evening connection to the BKK flight usually puts you right beside your connection.

Connections to SEA are a bit hit and miss - on a 50 minute connection, landed 20 mins late, I was dumped at a remote stand, bussed to Area A, and was then refused any help to get to area C. Screamed blue bloody murder when I found my flight had closed, but not departed - so they re-opened security at the gate for me. I was ready to slaughter all and sundry!