We investigate from first principles the proposed destruction of the controversial e(')g pockets in the Fermi surface of Na(x)CoO(2) due to Na disorder, by calculating its k-dependent configuration-averaged spectral function <A(k,ω)>. To this end, a Wannier function-based method is developed that treats the effects of disorder beyond the mean field. Remarkable spectral broadenings of order ∼1 eV are found for the oxygen orbitals, possibly explaining their absence in the experiments. In contradiction with the current claim, however, the e(')g pockets remain almost perfectly coherent. The developed method is expected to also generate exciting opportunities in the study of the countless functional materials that owe their important electronic properties to disordered dopants.