Sort of knew that would be the answer. When you look inside an LM-1,2,3 the track power wires connect to four SMD power diodes that form a bridge rectifier. The DCC AC signal is immediately rectified into DC upon entering a LM. The LM is effectively being supplied PWM DC when operating on DCC. With a 50% duty cycle oscillator as a stand in for the DCC command/booster, the LM would see a 100% duty cycle PWM signal. No different than a DC power supply.
The AR-1 definitely will not work with DCC. The input side of the AR-1 is polarity sensitive (marked on the unit and called out on pg3 of manual) so feeding it the DCC AC waveform is out of the question. Plus, as you rightfully mention, it would be a very expensive frog juicer.
The DCC appliances on the market (juicers, occupancy detectors, and the like) are made to work with an AC square wave on the track. Providing the unit is not DCC programmable, there isn't any reason why the duty cycle or pulse width of the AC wave should make any difference. Ironically, it is this square wave that is at the root of the DCC dirty track problem.