I have successfully setup a WP site as a FB app using your plugin (awesome)
I have also now gone a step further and encountered an issue I hope you may regard as a bug or future upgrade.
I have made my WP site members only (login on front page to access home) - then I have used another 3rd party plugin to authenticate my WP users from an external database.
This works well.
(note: my WP site is for members of an existing web service)
Now, I have tested all this is facebook - the FB app canvas correctly shows the WP login page if the FB user does not have a logged in session in their browser for the WP site.
In the FB app you can login to the WP site. - and here is the issue:
After login, the FB app shows the proper WP home page (not the FB styled version) - so I guess its just the WP site home page in an iframe.
If I then refresh the FB app canvas it loads the correct FB app canvas look of WPBook
I hope all this makes sense. It might be better to see it all in action