Ad Badger checks that a keyword does not already exist in the destination ad group before adding it. If it is sourced from two different ad groups, it will only add one of them. 

The Hunt will not add the same keyword on the destination ad group whether it's active or paused. It would be best to select the right destination Ad Group for proper organization of your advertising. It would be easy to monitor and optimize if you have set the right destination Ad group for PKW hunt. Hope that helps!