In most situations, ATC will advise the availability of the ILS and any differences from the promulgated category of approach that it can support. After implementing LVPs, a Cat II/III ILS can be used to the relevant minima. As a controller, I have never cleared an aircraft for a Cat I, II or III approach, just an ILS approach - in broad terms it's up to the pilot to determine whether everything that is needed for his/her operation is in place.
As a principle, I think this is the general case but if the controller did clear an aircraft for something that is not published, presumably it is something agreed locally and written up in the procedures of both ATC and the aircraft operator.