From what I understand, the VRM has a peak current rating of 2 amps and a continuous load of 1.5 amps, and the radio has a 1.5 amp draw. Bit of a design oversight in my opinion, because if your robot has any other electronics that need a regulated voltage, you need another module.
For LED ring lights, I suggest you run them straight off the PDP, unless they aren't rated for 12 volts.
http://content.vexrobotics.com/vexpr...e-20141230.pdf
look at the bottom of page 7