Questions about P vs NP and geometric complexity theory
The short answer is no these are not known, though they are certainly not out of the question. There are no direct implications known to P vs NP, and we do not even have a conjecture (let alone theorem) that such-and-such a representation is an obstruction iff $VP \neq VNP$.
One can start to get at an implication to ordinary P vs NP by trying to implement GCT in positive characteristic, using the polynomials from GCT I that more closely capture P/poly and NP. Since poly-size Boolean circuits are equivalent in power to poly-size algebraic circuits over a finite field, this would actually show NP not in P/poly. However, in positive characteristic both the geometry and the representation theory get harder (and it's not even clear if multiplicity is the right notion any more, because one is then dealing with modular representation theory, where representations need not be completely reducible).
Even in characteristic zero, we don't know the &quot;general converse&quot; about obstructions, namely, we don't know that $VP \neq VNP$ implies existence of multiplicity obstructions. But we do know that if $VNP \not\subseteq \overline{VP}$ then a separating module (equivalently, HWV obstruction, see Bürgisser-Ikenmeyer STOC '13, arXiv) must exist.