If I check a bag and my flight arrives Copenhagen airport at 11:20 AM, will I have time to deplane, claim luggage and get through passport control in time to make a train departing the airport at 12:23 PM?
I suppose its theoretically possible; possibly a bit more likely than my getting elected President.
It is not something I would try to do.
Where exactly are you going with the train?
The 12:23 train from Copenhagen Airport is bound for Nivå via Copenhagen. These trains go every 20 minutes.
Gregory, Where are you flying from?
The answer to that question determines whether you will have to go through immigration (passport control) and how likely the flight is to be late (the longer the flight the more variables).
BTW, passport control is normally before luggage reclaim. Any time spent waiting for passport control is time you don't have to spend waiting for your bags to appear.
I have no experience of Copenhagen airport, but I would say 1 hour is too short for any airport anywhere, even if you don't need to go through passport control.
I would say it is doable, with a probability of 70-80 % that you will get to your train in time. Could I ask where you plane originates? Try to be seated in the front of the plane to get first at passport control if your plane originates outside Schengen.