You can use an external supply to power the ColorDMD but you need to be very careful that the DC output of the supply shares a common ground with the game ground. If you're not careful, the supply may be floating relative to the game ground (or worse), and can cause damage to boards because the ColorDMD is connected through the ribbon cable to other boards in the system.
There's also a possibility of ground loops and ground noise which could cause data errors across the video ribbon cable.
If given a choice to move LED strings or the ColorDMD to an external supply, always choose the LED strings as they don't generally require a common ground or interact with other boards in the system.