I managed to have a custom post type use the default categories and be displayed on the default WP archives. When selecting a specific category within the Genesis Featured Widget Amplified only posts from the chosen category not the custom post type are displayed though.
And selecting the custom post type in the widget options instead of the category doesn't show any of the posts of the custom post type neither...
Also Is there a way to show a specific category AND a custom taxonomy in one widget at the same time? Right now you have to choose a specific category or a custom taxonomy.