The page you link to is a little bit hard to read with all collapsed sections. In "Where is the test centre located and what are the opening hours?"
The test center is located outside at parking P5
So you can't use the "test center" to pass border control.
In "New requirements for persons from high-risk countries"
- A service provider has facilitated a test facility in Pier E and in Pier C, so that passengers arriving without a valid test result can be tested. This test can then be used for documentation at the border control.
- We would strongly encourage passengers to have a Covid-19 test performed before arrival in CPH, so that there is as far as possible assurance that they are not infected on arrival in Denmark.
- Passengers residing in a high-risk country that gets a positive test result in CPH will be handled by the authorities
So there is a rapid test available if you can't perform it before you go. It is not recommended though.