Moving your post to the JFBConnect Pre-Sales page after post this.
Yes, you can easily show your site within a Facebook Page. With JFBConnect, you'll be able to easily select a special template to be used only when your site is shown on Facebook, so that it fits and looks good there. Also, JFBConnect lets you (optionally) create a "Reveal" page where a user would have to Like your Facebook Page before they could see your site within the Facebook Page.
That's in addition to a ton of other features.
Hope that helps, but if you have other questions, just let us know.
Thanks,
Alex