ok, here is the link of the ARDUINO compatible board we are talking about, the COLORDUINO:
http://iteadstudio.com/product/colorduino-v1-3-preview/
and here you can find schematics both from the whole board, and from the led driver chip itself:
http://iteadstudio.com/produce/colorduino-schematic-and-demo-code/
It this then clear, that something simple like this won't work:
as there is no common ground, but both ground and positive are switched on and off by the controller.
Maybe something with NPN transistor on the 8 Vcc pin(LED's common anode), and PNP transistor for the 24 RGB pin?
mumble mumble... 