I think we all have to assume that it doesn't. Only the brief header of your FB page is visible for Google. I wonder whether there is a way to insert your external website link into your FB page so that it would show in that header.
Well... if you've got a link in that part of your Facebook page that shows publicly, meaning without the need to log in, that link will be indexed then. They are "nofollow", but I'm pretty sure that googlebot disregards the instruction in this particular case.