Certainly on our route network (Europe) there is no requirement to tell ATC. It doesn't change anything for them, and therefore they're not interested. We used to do it, and would invariably be met by silence, then a confused 'Roger' and occasionally a 'LVP protections are not in place.' It may be different in other parts of the world of course
My understanding is the same and I experienced likewise. OTOH, ATC at some airports seems to have their own set of NON-LVP autoland procedures that can be helpful to aircrew too.
The 777 incident in Munich was a case of autoland gone wrong in non-LVP (protections not in place) situation, yes. Factual report
here from BFU.