Re: asbestos, how will you handle putting holes in the old floor, e.g. for the 3" drain pipe?
As to the underlayment, I don't really have an opinion, but I think the principle concern should be the compressability of the layers between the bottom plate and subfloor. If you are going to use threaded rod to put the half wall in compression, then perhaps it is better to put plate on the vinyl and just let it compress. If you aren't, perhaps it is better to run the plywood under the plate, so the vinyl will compress less. But I don't really know.
BTW, my sheet goods installer recommended 3/8" underlayment, but I suppose that it may depend on the smoothness of the existing floor.
Cheers, Wayne