Powering the extra LED from the existing ones would be easy, as you said, but the questions is where are you going to place the LEDs? Every Cherry MX switch already have the little holes that are used to place the LEDs, but those are supposed to have holes on the PCB so that you would only stick the LED pins through the switch and through the holes on the PCB. The 6G PCB does not have these holes, and you can't just drill them because you will destroy the copper traces that are on the PCB. Also, the switch mounting plate is in the way, which means you will probably have to desolder every switch to remove the plate from the PCB and that is a very long and tedious task.
All in all, I'm sure it is possible with some careful wiring, but you will have to be very eager to have those extra LEDs to justify all the work necessary.
Btw, do you have a 6G or 6G v2?
EDIT:
http://geekhack.org/index.php?topic=43241.0 this guy did something similar, but without desoldering the switches.