Using Public IP addresses for Private Network
RFC1918 outlines the IP space that should be used for private internal use.
It sounds like you already know this, but users on this network will not be able to communicate with any devices that are on the real 192.192.192.0/24.
Also, as @voretaq7 points out in chat, your registrar might be none too pleased with you using public IPs that aren't yours.