I bought an RGB LED strip and some white frosted window screen to experiment with. I still don't have a proper background box, or even filled my small test tank with water.
Unfortunately I suspect that white window screen may not work well for a reef tank. The idea was that the blue LED light should color the white screen, but that means any darker background areas (like the bottom and side edges) may still look white. In a reef tank you want the dark areas to be blue, and the bright area near the water surface to look white, not the other way around.
LEDs may still be useful combined with a blue screen, at least if the LEDs are bright enough. My LED test strip is 5m/15' long, and uses 23W (with white light, colored light probably uses less). In a 120cm/48" long background box I'd have to cut the strip into 4-5 pieces and install them in parallell, but I'm still sceptical to how much light you'd get compared with a 54W T5 tube.
At least the LED color control is great. You can really fine tune how much green you want in the blue light, and also dim it all if necessary.