Because killing the update.exe process through task manager didn't work
(access denied), I decided to reboot the machine.

I wish I hadn't: it now hangs during booting, with the progress bar approx.
3/4 of the way (in the graphical boot screen, not the text one).

A data disk (no system files on it) was replaced only yesterday, and after
that all its harddisks were chkdisk'ed and the system successfully rebooted
an extra time after all tests, nothing was wrong then.  The event log was
clean too.

It's a plain simple fileserver, only the OS itself with all previous
updates and 2 pieces of software installed: Apache webserver and SubVersion
version management system.  Neither of those two uses the MMC (what the
update seems to be for).