You don’t need ATC’s permission to do a CATII/III approach, however, if low viz procedures are not in force, the ILS you are using may be subject to interference. When low viz procedures are in force, ATC will notify on the ATIS and aircraft are kept clear of ILS sensitive areas near the runway, thus preventing the interference.
It would certainly be advisable to advise ATC you were completing a CATII/III approach when not in low viz, but you must be aware of possible errors in centreline and glide slope tracking, which could ruin your whole day if caught off guard in marginal conditions. Better to practice them in CAVOK.