Yes, they do. I ended up finding a much easier fix than messing around my BIOS, which is to disable the brightness setting in Synapse 3. It turns off the LED's, even when my PC is off, until the setting is checked again.

Do they turn off if you unplug the usb cable? If that's the case you could try checking your BIOS options to turn off usb ports when your PC is off, or trying another usb port - maybe not all of them are powered 

Hello,

I am using the Razer HDK Chroma externally for additional lighting behind my monitor, and it's pretty inconvenient that they don't turn off when my PCis off. Aside from unplugging it from the AC power plug and therefore reducing the brightness by about 10%, is there a way to make sure that it turns off when my computer is off?

Thanks. 

Help with Chroma HDK?