if by 'Elgg Website' you meanthisElgg website, then no, it's set up to be public.
if you mean yoursite then sure, you can use the 'restrict pages to logged in users' option in admin settings if you want everything locked out, or you can add a gate_keeper() call to profile pages if it's only profiles you want to protect.
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Security issues should be reported to security@elgg.org!
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