If so, that's too restrictive. The interaction between two He atoms needs QM (dispersion forces). Heck, even two water molecules interacting is a QM even if you decide to classify the polar attraction as purely classical. You'd still be omitting a lot of the interaction energy.
I see no way I can simulate catalyzed (enzyme) breaking of a chemical bond without:
Well duh, my point is that Newtonian physics is a subset of QM, but doesn't need to be. In fact it's an important result in QM that QM becomes Newtonian in the limit.
Chemistry, on the other hand, is QM. All of it. You can empirically get around it like alchemists did for a while. But it sucks.
This is partially why chemists accepted the existence of the atom far (far) earlier than physicists who stuck with continuum theories - their empirical methods were banging against the wall.
A chemical system is necessarily QM. Chemistry is either purely empirical, or quantum.