Being 'private' only means you don't get hit by drive-by scans from the Internet. There are (depending on configuration) plenty of opportunities for internal attacks, for example the workstation being used to access the boxes. Not to mention removable media (usb, cd-rom) or files copied onto those otherwise isolated hosts could be infected.
Patching servers is just good practice. As is designing a system that can handle rebooting individual servers without user-facing downtime.
Patching servers is just good practice. As is designing a system that can handle rebooting individual servers without user-facing downtime.