Nope, that's not required. The only thing you can do with your Facebook Page is now use the JFBCFan module to have people like it directly or see a feed of your recent posts on the Page. Pages and Applications are different beasts altogether, and they work separately, but there's no issue using both for the same site.
Finally, for the App Directory, it's your choice to join the directory, and there's information you can find about the directory on Facebook itself. Being in the directory won't change JFBConnect in any way.
Hope that helps!
Facebook Application
