Re: Would it be legal/possible?
 

Yes if the gauge of the wire used meets the minimum for the breaker feeding the circuit, or if you provide additional circuit protection appropriate for the gauge of wire in the circuit.

Of course connecting it only to the PDP you'll be stuck with only Red, Blue, Green, the color that will result from driving two of those colors at 100% duty cycle or white if you connect all three grounds.

Now there is nothing that says you can't use a micro controller and some transistors to create a custom circuit to very the duty cycle of the separate colors.

Re: Would it be legal/possible?
 

Yes, but you would not be able to have the colors change without relays or other switching. If you aren't interested in "shades", but just being able to switch among the eight colors (off, red, green, blue, magenta, yellow, cyan, white), you can use 3 DIO ports and a relay module similar to the following:

http://store.linksprite.com/dc-5v-four-channels-relay-breakout-with-optoisolator/ (You would only need to use three of the four relays). We are planning to do something very similar to this to display our alliance colors during matches, green (our school color) during practice, and perhaps a few others occasionally.

Re: Would it be legal/possible?
 

Consider rule R34 if you're planning to connect directly to the PDP.

Re: Would it be legal/possible?
 

As others have said, "probably", but please remember we are not official rules people, and our opinions (which is what these are) are completely worthless at any competition.

That being said, having an RGB light strip connected directly to power is a waste, these have such great capabilities for color display, a direct connection gives you "one color only", you can choose from 7 colors + "off" depending on which grounds you connect.

Re: Would it be legal/possible?
 

Another question on the same topic. Is it legal to put in dongle such that you can switch between two different colors. We don't want to spend to much time with the leds this year