Does the Denmark Eurail Pass cover Copenhagen Airport to Kobenhavn Station?

Yes, you can use it for this route! However, if you only make this journey on your first (or last) travel day, I'd advise you to buy a seperate ticket. You have two options:

• DSB train Copenhagen Airport - København H
• Metro Copenhagen Airport - Kongens Nytorv (or whatever metro station suits you best)

As @Mattheas  said this trip would need a travelday of your flexipasses and if it´s your only trip on that day i recommend to use the local offers as mentioned above.

Thank you