I suspect, but can't prove, that the answer is "No", as materials are meant to be portable. However, I don't see why we couldn't implement something that would at least look up the vertex group name to be sure and return a default value otherwise.
I'm working on some very visceral-looking alien architecture, and I assumed that I could use a vertex group (and its associated weight painting) as the factor input to a mix shader. However, when I go browsing through Input nodes for my material, even though I could swear this was in there at some point, I'm coming up with nothing.
I may end up doing something complicated involving a custom property and a sequence of drivers here, if I can't find it. Seems overkill for a material, but thems might be the breaks.