Visible light is just the part of the electromagnetic spectrum that we humans can see with our eyes, but that doesn't make it any less kin to radio waves and other radiation types (gamma, X-ray, ultraviolet, visible, infrared, microwave).
In other words, there is no conceivable reason for it to not be able to transmit data, provided the right system is in place.
Sure enough, data transmission through visible light was actually invented a while ago. Unfortunately, practical implementations are still a no-go.
That doesn't mean people aren't trying though. In fact, Japan-based Outstanding Technology has introduced the Commulight location system, which gives smartphones and tablets downloading info through photons instead of radio waves.
There are two dongles: one of them has USB, while the other goes inside device 3.5mm jacks. Integrated sensors access location-based information from an overhead data-transmitting LED.
Possible uses of the system include indoor alternatives to Wi-Fi and GPS, coupon transmission, information exhibition in museums, etc.