"Does it require a CATII or III ILS or can the aircraft remain current on a CATI practice autoland?"
As I understand it, airplane CAT III Autoland currency can be maintained with a CAT 1 runway and Cat 1 weather conditions. As long as the aircraft lands the way it should, there should be no problems with currency.
Note that the airplane systems don't know what the visibility is or what type of ILS is available at a particular airport, so these are ignored from an airplane point of view.
From the point of view of aircraft system serviceability, however, the systems must meet the required minimums for Cat III autolands (wrt to redundancy, electrical bus isolation, etc).
Rgds.
Q.