The simple answer is no. At the moment Fabrik only offers the capability to password protect projects.
If your reason for wanting to password protect your site is because you are currently building your site and worried about people seeing it. As long as your site is still on the .onfabrik.com domain initially provided and you have not giving that address out then no one will be able to find your website to see so you do not need to worry about that.
If for other reasons please let us know.