The login form from the docs works fine and so does the password reset. However I have been unable to register a new member or show a logout link, this is the same issue I had whilst using the AUTHENTICATE module and came to the realisation that as CORE doesn't have the member module the logout and register wouldn't work (took me three days and I'd rather not spend the next three days trying to get this to work.
FreeMember simply provides a nice way to generate templates for the existing member functionality built into EE. EE core doesn't include any member functionality.
So no, FreeMember doesn't work with EE Core and never will. I doubt any other member modules would either, and if they did, I expect they would have dubious legal status.