There's a subtle difference between 'using' and 'supplying' magnetic variation ICT_SLB. Inertial systems - whether FMS's utilising separate Lasergyro INU inputs as used on most large airliners, or self-contained General Aviation systems such as Honeywell's LaserRef products - do their navigating by reference to True North and produce magnetic variation outputs for external use only. The conversion in all variants is done using mag/var tables stored in memory. The updating frequency for the magnetic variations depends upon the technology of the system. As BOAC points out, old 'steam driven' Delco Carousel or Litton systems are hard wired and long out of date, whereas FMC sofware based tables may be updated as often as once a month. Neither method can ever be truly up to date as the data is only as good as the latest global survey.
BTW, those VOR and ILS systems that you mention are already scheduled to be de-commissioned under the long-term strategic plans for international ATC. In due course all ATC, including long-haul en-route navigation, will be under Area Navigation rules based on a combination of short-term inertial accuracy and long term GPS correction. When this is implemented, given the availability of cheap GPS systems for general aviation use, I still see no further use for inaccurate magnetic headings.