I made measurements a while back. Yes there's a slight voltage (or perhaps "current" is a more appropriate description). I don't know why they'd design a circuit that doesn't present a real open circuit. It's not a problem for incandescents but it's a problem for some LEDs. A 10kohm resistor in parallel with the LED should help swamp out the current.
I originally though the remnant power was from an analog ramp to brighten and dim the bulb but it turns out they ue "pulse width modulation" to make the bulb appear as a varying brightness with full-on and full-off power levels.