Researchers from Georgia Institute of Technology are developing new approach for using pentacene combined with buckminsterfullerene in solar panels.[2] Pentacene is also a subject of research for use in organic thin film transistors and OFETs.

Pentacene is one of a series of linear acenes, the previous one being tetracene ( four fused benzene rings) and the next one being hexacene (six fused benzene rings).
-From Wikipedia

I agree with your premise and that the studies would have to be conducted but again, as I mentioned in my comment earlier, here we are neither dealing with high voltage, nor high power - just enough to run your iRobot Scooba cleaner, flat screen TV, cell phone, PDA, notebook computer and floor lamp.

We already live in a world that is pervaded by electromagnetic fields and studies from decades ago found issues with pregnancy and monitor usage that was well documented (lawsuit material).

This is a product I would never allow in my home or office until the medical implications are thoroughly studied.

Have they tested the effects of the inevitable electromagnetic fields on humans?

Tony,
As far as I know, no, they have not. But this should not be an issue in this case.
First of all, these sheets are designed to deliver power only when the electric device is near and because they use microelectromechanical switches, this power is delivered via the grid of copper coils using the shortest path and thus the entire sheet is never fully under voltage. So it when your computer is getting charged via this material, it produces as much EMF as your regular power cord would.

Second of all, the currents that can run thru these sheets are relatively small - up to 80 watts.

And lastly, the EMF become harmful when their frequencies increase which enables them to travel further. In case of this “tablecloth” power charger we will be dealing with our household grade 60Hz; [Actually I am wrong here it transmits at 13.56MHz] whereas, your cell phone, for example, is around 1900 MHz.

In original research paper published in “Nature Materials” there is a picture of a fish tank with a live fish inside. The LED lights in the tank are powered using this transmitting material. Power cables, sockets, and plugs are not required, and all of the metallic parts are coated with insulating materials. So I’d say it is safe to wrap it around a head

Yes, this technology is amazing but there are also limitations. For example, I forgot to stress the fact the power cannot be transmitted over a long distance. The power-transmitting sheets are meant to be like a tablecloth for your desk where you put your laptop or cell phone, or I guess it could be in the floor tiles so your iRobot’s Scooba floor cleaner can always be charged.