  We have studied the effects of strong impurity scattering on disordered
superconductors beyond the low impurity concentration limit. By applying the
full CPA to a superconductiong A-B binary alloy, we calculated the fluctuations
of the local order parameters $\Delta_{A}, \Delta_{B}$ and charge densities,
$n_{A}, n_{B}$ for weak and strong on site disorder. We find that for narrow
band alloy s-wav e superconductors the conditions for Anderson's theorem are
satisfied in general only for the case of particle-hole symmetry. In this case
it is satisfied regardless whether we are in the weak or strong scattering
regimes. Interestingly, we find that strong scattering leads to band splitting
and in this regime for any band filling we have a critical concentration where
a superconductor-insulator quantum phase transition occurs at T=0.
