Possible, yes. And yes, LED are efficient, but so is mercury vapor and the rest. And efficiency isn't that important in printing. LEDs are expensive and they are very much a point light source. This means that there needs to be a lot of diffusion. Diffusors are inefficient. So it could be done and if you wanted to use all your spare time for a couple of years, you could probably make one that as good as one you could buy today for less money. Better off taking more pictures.