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For a modulated carrier at 100% modulation 2/3 of the power is in the carrier and 1/3 in the modulation. If the LEDs only see the 50Hz (which I doubt is actually the case) what happens to the carrier power? Well I believe it goes to heating the LEDs which would explain what I found in my experiments above, post 33.
No, the lamps will either have a simple current limiting resistor or a switching regulator in the case of 12V modules, but neither methods care about the input waveform - once rectified and filtered by the main input capacitor, the LEDs or the driver see plain DC. The input waveform is integrated in its entirety less losses of the rectifier diodes and heating due to the ESR of the capacitor.