geohei,
I can only refer this to the boeing 737 under UK CAA rules at the two uk operators I have flown them for. For approaches below cat 1 minimums (normally 200ft decision/550 metres RVR) we have to make an auto land, we are not allowed to fly a cat 2 approach to a manual landing.
However, this does not allow a landing below cat 2 minimums in LVOs on a cat 2 runway. at cat 2 decision height we must have sufficient visual reference to land, this means that the approach can be monitored visually to ensure the aircraft is properly positioned in the touch down zone. Don't confuse the autopilot being engaged below decision height with landing below minimums, the first is fairly standard even for a cat 1 approach in very marginal conditions, the second is illegal, foolish and dangerous.
There may be other technical limitations for different aircraft and airworthiness authorities, I believe that the FAA allow manual cat 2 landings for the 737, for example.
Although as longhitter states there is no need to be cat 3 qualified the crew would have to be cat 2 qualified. I suspect that most operators of cat 3 capable aircraft will have low vis ops approval that covers cat 3 and cat 2 also. Some aircraft types can only operate to cat 2, in which case that operators LVO approval will only cover cat 2, not cat 3.
Also, a few cat 1 airfields may specify that autolands cannot be carried out, but that will be stated somewhere in the airfield briefing charts, I can only recall seeing that once and can't remember where it was.