Problem crawling site due to user restrictions

I want to back up this site on an extranet, that is like a multisite behind a walled garden.
I can temporarily remove the log in requirement, but I still have some content hidden that is only visible for logged in users.

Is there a way to log in and generate a static page as a logged in user, or is there a way to tell whether the page is visited or pulled by Simply Static?

I basically just need some way to do the check if it is the plugin/localhost that is pulling the page so I can make an exception in the scripts that hides content.

Grateful for any help