Does a dimmed LED lamp draw less power than one at full brightness?
It depends on the LED driver, but unless it's of a bad (or very specific need) design, a dimmed LED lamp will draw less power.

Usually, dimming on LED lamps is done by PWM (Pulse Width Modulation). The LED will actually turn on and off faster than the eye can see. By modulating the ratio of the time the led is on and off, it simulates the dimming to the human eye. 

This method is widely used because it is the cheapest and easiest method to dim an led but it can also cause some eye fatigue. 

With this method the power will reduce with the light intensity (or perceived intensity).



Another method of controlling the light intensity of an LED is to control the current flow through the LED, and there are mostly 2 ways of doing it:


Through DC/DC conversion like a current controlled buck converter or similar circuit.


in this case the current will reduce with the intensity of the LED. With this method, there will be little flicker, which will be roughly equivalent to the DC/DC converter ripple.


Using an analog ballast (adjustable current source), like a transistor, mosfet or specialized IC with required regulation.


In this situation, the current will diminish but this circuit will likely have more losses.

The latest has the advantage of providing a very stable light intensity (if needed for some specific application perhaps like photography), so we can imagine this exists on the market.



The power will be reduced when the light intensity is reduced, but it's not a linear factor. F.I. 50% dimming might not have a 50% decrease on the power consumption.

The reason is that the control electronic will have some non-linearity and won't have the same efficiency at different operating condition and the second reason is that the eye intensity response is not linear to the actual light.