But if you have that static page redirect to the category, then it would work. This is a perfect situation for using page redirects to blend pages and categories. Make a page that introduces the category, and have it set up to redirect to the category page URL. Then have that intro page display on the featured posts. The category introduction page will then display in the featured posts, but when the link is clicked, they will be taken to the category page rather then to the static page.
Currently, I am using the "Quick Page/Post Redirect" plugin to accomplish this. Once it installs, it displays a URL redirect window right under the page edit area. Simply have the category intro (static) page redirect to the category (page). The end result is that you are now able to virtually display categories as featured posts, as well as mix pages and categories in drop-down menus.