If the admin can see the IP address, then the network and other services on the network can also see that address.

It sounds like, to me, that the person has managed to create a vhost address which does not display. Exactly how they did this (if in fact this is what they have done), I'm not sure.

If they have set a vhost that consists of non-printable characters, then it would appear to be invisible or missing.

Examples of non-printable characters are
$chr(2) Ctrl+b Bold text
$chr(3) Ctrl+k Colour text
$chr(15) Ctrl+o Normal text
$chr(22) Ctrl+r Reversed text
$chr(31) Ctrl+u Underlined text