NO. And why would you?! Your website is your website, and your fan page is just that, your fan page. Fanpage Connect formats individual pages for your fan page tab.
I have built a separate mini-site version of my site using a multisite install of WordPress and the mini-site is on a subdirectory install.
I want to include a special fan-only content area in a widget above the header that would display across the mini-site. Would you have any tips on how to do this?