Quantum Mechanics is why atoms and molecules exist and form bonds. QM is the physics of chemistry. Without QM, chemistry does not happen. The universe would just be a big churning mess of particles and you would never get little lego pieces that snap together according to repeatable rules that, when repeated, form macroscopic substances of innumerable description up to and including life itself.
So QM is no doubt involved, but on this scale it is either a trivial fact or an indication that someone tried to lean on a classical approximation, it broke, and they had to revise it (which arguably says more about the approximation than it says about the underlying behavior).
Apologies for the nitpick. It's a pet peeve of mine that discussions of QM tend to focus so hard on the strange behavior that they forget to mention where QM fits into the bigger picture and leave people with the impression that it only matters under special circumstances when in fact it matters so much that you can hardly have "matter" without it.
------------
Re: anesthetic, a large fraction of simple halocarbon compounds have intense neural effects, so anyone doing halocarbon chemistry would quickly be put on the "scent" even if they weren't tasting everything in the Sigma Aldrich catalog.