There was an interesting paper published recently on the effects of accuracy on annealed cases, or rather, the adverse effects due to case hardening. The conclusion was that annealing does improve accuracy and there was a lengthy explanation as to why.
From a personal point of view, based on annealing by hand, I hadn't noticed any spectacular improvement. However, since a mate of mine acquired an AMP machine and has annealed some cases for me, I have noticed a definite reduction in vertical dispersion.