Yes, multiple tests have shown that LED lighting fixtures can transmit wireless data at very competitive high speeds. A commercial product started shipping several months ago.
What if every light bulb in the world could also transmit data?
Li-Fi is here. pureLiFi shipped its first fully wireless optical networking systems in the fourth quarter of 2014. The product, Li-Flame, turns standard LED fixtures into wireless Internet access points. Just like the theory said it would.