not quite !
you can't use the strain for a linear analysis to infer much of anything about the non-linear state.
the reason is the change in stiffness as the material goes plastic, which redistributes load internally.
to follow your proposal, if you mean to replace the linear stress with a stress deduced from the stress/strain curve for the linear strain, then you've just removed a lot of the internal strain energy of the model, and this has to be added back somewhere, somehow. NL FEA works by figuring out the point of plasticity, then incremently adding load changing the stiffness of yield elements.
Quando Omni Flunkus Moritati