Hi JammedStab;
CAT II/III have specific requirements which are different from "normal" ILS approaches, (ie, CAT I). Differences may include an ATC announcement that "Category two (or three) approaches are in progress", ILS LOC/GS transmission standards being assured to be CAT II, standby airport power is operational, airport traffic at/near the approach runway, in-trail distances for aircraft on approach etc. Likely ATC would not issue you a clearance for a CAT II approach if the weather does not require them and the airport is not deemed to be conducting such approaches.
You can practice CAT II procedures on any day on any normal ILS providing you're prepared to take over immediately if the autopilot isn't doing what is expected - there is the possibility the autopilot may do this due to the above standards not being adhered to if CAT II ops aren't in progress. Some OpsSpecs are silent on an autoland off an ordinary ILS but I would not encourage it as the guidance may not be suitable for autoland. However, it is good to practice CATII procedures as you may not see them for years. In 35 years I've done around five or six of them in various types for real and it is a remarkable process each time - I can recall brilliant sunshine until we entered the fog at around 100ft. The RVR was < 600ft, the autoland, (CAT IIIb) was on an A330...(the RVR equipment couldn't measure lower). It really reinforces trust in the autoflight/autothrust/autobrake systems. The trick was in finding one's terminal...
Here's one reference that may be useful:
http://www.tc.gc.ca/media/documents/...ns/TP1490E.pdf