This is really a trick question. "No" should be correct—a plant can't stay alive without a regular dose of light—but it isn't entirely correct. Yes, plants do need food to survive, and yes, they generally get this food through photosynthesis. However, experiments have shown that it is theoretically possible to keep a non-photosynthesizing plant alive, at least for a while.
John S. Boyer and his coworkers at the University of Delaware have kept the developing kernels of corn plants alive and growing in a low-light environment by feeding them sugar water. The sugar water, which was fed to the plants intravenously, sustained the growing kernels for five days. Without the sugar and light, the kernels would have died within a day.