dont think the led will induce hum, theres no ballast or filament involved
closest i have seen is actually blinking led those with mutiple colours which blinking rate kinda of bleed into the audio path of pedal and gotten amplifed thru the amp. Hehe, imagine a loud amp at jamming volume and without playing the instrument, you can hear the hiss from the loud voulme, going in rhythmic pattern according to how the led blinks
.
The above case just a minor thingy thou, coz when the instrument is being played, cant hear that hiss already..
and for fun, putting a wah pedal after such pedal with blinking led, up the volume and rocking the wah pedal will do a pseudo sample and hold effect in fixed rhythm/rate pattern...