If a live server is required to be rebooted, with no changes being made, should an RFC be raised (either upfront or retrospectively) according to the ITIL process?
Per the ITIL definition, yes, a RFC should be submitted for a server reboot. An ITIL Change is defined as the change of status or attribute of a Configuration Item. Even if you don’t have a formal CMDB, most people would agree that a server’s status and attributes should be tracked.
Rebooting a server takes the status of the server from online to offline and then back to online.
I would hope that a mature Change Management process would handle this as a Standard (pre-approved) Change or a Minor (the Change Manager has the authority to approve) Change. Having every server reboot go to the CAB could needlessly weigh down the process.