Are hash onions inherently sequential?
For all engineering purposes, you are right, if you choose a cryptographically strong hash function $H$.

For theoretical purposes, nope.  There's no proof.  Your argument is based on unproven assumptions, hence it can't be regarded as a proof that NC $\ne$ P.  In particular, we don't know of any hash function $H$ that we can prove is cryptographically strong, or that we can prove is inherently sequential when repeated like this. All of our hash functions are either heuristic (we think they are good but we have no ironclad proof) or are based on other assumptions (such as that factoring is hard; something we suspect but have no proof of).  And assuming that $H$ behaves like a random oracle is an unproven assumption.  So if you're a theorist and what you care about is proving that NC $\ne$ P, none of these count as a suitable proof.

Personally, I do consider them pretty good evidence that in all likelihood NC $\ne$ P... but it's not a proof.