Well, apparently, it is possible, as scientists and engineers at Cornell have done it! These have all the wonderful properties of OLED's, they're flexible, they produce a lot of light per watt, and they can be mass produced inexpensively. But also, when exposed to bright light, the reaction is reversed, and a current flows out of the OLED instead of into it.
So now, OLEDs can be both an energy collector and a light emitter, depending on the needs of the consumer. Imagine your cell phone's backlight collecting energy from ambient light when not in use. Or your windows collecting energy during the day and then producing light at night.
Soon, OLEDs may offer both low-cost lighting and low-cost energy production. A paper on this subject was just published in the journal Science, in which the Cornell researchers recognized that they needed to discover ways to make the photovoltaic reaction more efficient before it can be mass produced.