Can newly created users with Administrator role log-in to BIG-IP even if there is remote authentication configured?

tested this and it works as expected. once you enable remote authentication your existing local accounts / passwords don't function anymore. all requests are forwarded to the remote auth server.

you also can't create any new local admin (or any other) users at that point.

so indeed if you disable your admin / root account then you will be locked out, so don't :)