We present the results from an extensive atomistic molecular dynamics simulation study of poly(ethylene oxide) (PEO) doped with various amounts of lithium-bis-(trifluoromethane)sulfonimide (LiTFSI) salt under the influence of external electric field strengths up to 1 V/nm. The motivation stems from recent experimental reports on the nonlinear response of mobilities to the application of an electric field in such electrolyte systems and arising speculations on field-induced alignment of the polymer chains, creating channel-like structures that facilitate ion passage. Hence, we systematically examine the impact of electric field on the lithium coordination environment, polymer structure, as well as ionic transport properties and further present a procedure to quantify the susceptibility of both structural and dynamical observables to the external field. Our investigation reveals indeed a coiled-to-stretched transformation of the PEO strands along with a concurrent nonlinear behavior of the dynamic properties. However, from studying the temporal response of the unperturbed electrolyte system to field application, we are able to exclude a structurally conditioned enhancement of ion transport and surprisingly observe a slowing down. A microscopic understanding is achieved.