UPDATE: I did some experimenting with the LEDs I got for my tail lights and here's what I found. With the running lights off, the LEDs work just like the incandescents and the corner lights blink with the main blinkers fine. It's when the running lights are on that things become tricky. The corner light doesn't light up, and the blinker function on the larger bulb gets dimly lit up. With the incandescent bulbs the blinker filament is heavy enough to act as a ground wire for the smaller corner bulb, but with LEDs both bulbs are trying light up and cant because the voltage is not enough to run them both in the same circuit.
Everything works fine with an led in the corner and incandescent in the blinker - it's the LED in the blinker that screws up the corner light.
Personally I'd rather have the blinker mod over the LEDs, so I'll probably just stick with the incandescents (even though I hate how the orange paint flakes off the blinker bulbs).
I think the only way to make the corner light blink with LEDs is to add separate bulbs for turn and marker, or eliminate using it as a marker altogether (which probably isn't legal)