Think of search engines as just text-only browsers.
Like any other browser user, they would have to register and login in order to walk through the restricted areas of the site. They don't have the capacity to remember millions and millions of logins.
Even if they could get in, ones like Google also contain links to their cached versions of a page which would defeat the purpose of being logged in.
The whole idea behind securing sections of a forum or site is that it's not supposed to be publically accessible.