The potential of elastic antineutrino-electron scattering in a Gd-doped water Cherenkov detector to determine the direction of a nuclear reactor antineutrino flux was investigated using the recently proposed WATCHMAN antineutrino experiment as a baseline model. The expected scattering rate was determined assuming a 13-km standoff from a 3.758-GWt light water nuclear reactor and the detector response was modeled using a Geant4-based simulation package. Background was estimated via independent simulations and by scaling published measurements from similar detectors. Background contributions were estimated for solar neutrinos, misidentified reactor-based inverse beta decay interactions, cosmogenic radionuclides, water-borne radon, and gamma rays from the photomultiplier tubes (PMTs), detector walls, and surrounding rock. We show that with the use of low background PMTs and sufficient fiducialization, water-borne radon and cosmogenic radionuclides pose the largest threats to sensitivity. Directional sensitivity was then analyzed as a function of radon contamination, detector depth, and detector size. The results provide a list of experimental conditions that, if satisfied in practice, would enable antineutrino directional reconstruction at 3σ significance in large Gd-doped water Cherenkov detectors with greater than 10-km standoff from a nuclear reactor.