BTW - variation shader doesn't work in specular channel either ;(
I am sorry, but did you really mean specular channel? We only have reflection channel in Corona material and it does work there for me...
As for the variation shader in the bump channel, it is unfortunately super hard to make it work due to the technical limitations. :-( But if you check it in C4D, it's not possible there either.
Displacement channel works for me. The only place where it does not work is a render perfect sphere, which only has "one polygon" in C4D, so no polygon variation can happen there in Corona either if we want to stay consistent with C4D.