Are ATCs required to notify pilots when they use MVAs?
I'm not exactly sure what you are asking, but no, we do not notify pilots that we are vectoring in accordance with the minimum vectoring altitudes - because that is what we always do. ATC is responsible for terrain clearance during radar vectors, and pilots know this, so it is implied and understood that we use safe levels.

MVA's simply define the lower level for radar vectoring in an area - the lower level of our designated "box". Just like there is an upper limit and lateral limits as well, that we cannot cross during vectoring. MVA's are based on terrain and other obstacles, to ensure that terrrain clearance is always provided. You make it sound like MVA's are only used in special circumstances, which is not true. Vectoring at and above the MVA is completely routine and happens every day.

As for cross checking by pilots, MVA's are supposed to be published on a separate chart which pilots can use to cross check their assigned levels. The MEA is not used during approach, and pilots know this. In case of a radio failure during approach, if the flight is being vectored below minimum sector altitude (MSA), the pilot will climb to the MSA, even if the MVA is lower.

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