Nick 1
Depends on the RVR. If you are legal to start the approach and remain legal until the approach ban point, then you're ok. But you said Cat III in progress, so probably not due to the approach ban.
FE Hoppy
If the tech requirements are met and the weather is at Cat II minima, I'd look pretty foolish doing a go-around because of a temporary deterioration as I got to minima, when I could have done the Cat III. As an aside, my company require us to autoland from a Cat II approach unless there is a tech problem that prevents it. So, if the aircraft tells me it's Cat III capable, and the ILS/Airport meet the requirements, I'll be in the bar shortly after.......
