It depends on the voltage rating of the Resistor and then what power source you'll be using in the controller.
A 2v LED will need a Resistor if the voltage source is anything above it, like 2.5v, but a 3V LED would not need one, and it would also not be as bright as it could be, or depending on the LED just not light up at all.
Also, the LED+ spot on the controller isn't for wiring up LEDs. That's for the player LEDs that are already in the controller. It turns the Grounds on/off to light them up, so that spot should not be used for powering an LED as it is always on.
Typically the power source for the Sticks is used for LEDs, as ti's switched (turns on/off with the controller) and it's 2.8v. That makes TP27 a possible candidate to use for the power source for your LED, but Sony has changed how that whole setup is done on the VX6, and I don't have one here anymore for testing that TP27 theory out. You'd need to use a DMM on it and make sure that it was 2.8v when the controller was on, then 0v when it's off, then it could be used.