Can someone guide me whether this PVRC method of flange leak check - see attachment -has been approved by ASME ? Has it been covered under non mandatory appendices of SEC VIII or otherwise in any other code or publication ?

I would say no.
The PVRC method is not explicitly intended to be harmonized with ASME PCC-1 Appendix O (where the gasket stresses are to be obtained "from industry test data or from the gasket manufacturer"), however they are not incompatible- to my knowledge.

In the European works, EN 13555 is more advanced thaN PVRC but they follow the same basic approach. In fact, as is noted somewhere about PVRC, "The unproven hypothesis of a common intersection point with the Tp=1 axis for all the possible unloading lines has been proven wrong by experimental data." and this makes PVRC obsolete.