Alright, I have an update for you guys at John's request.
I tested on my layout last night with a full power drop (turned off the layout completely) while the locomotive was running with full sound and lights. Locomotives were at a constant speed, running solo, at about 50% power. Tested both LM-3S and LM-2S, both with external bridge rectifiers installed. Railpro power supply to the rails, and locomotive modules seeing 12.2 V at rest, 11.2 V at speed. Locomotives were ScaleTrains SD40-2 and modified Athearn C44-9W (with Kato motor).
When I turned off the layout I saw an immediate decrease in speed. The voltage to the module dropped immediately to 4.3 V. The sound and lights stayed on, though the lights visibly dimmed. The sound was unchanged. Motion stopped rather quickly and lights and sound stayed on for another 5-8 seconds. So John is right, there is definitely a drop in speed when power is completely lost.
While running on my friend's layout I hadn't noticed it that much because I normally would just stop the train I was controlling if the power to the layout cut out (happens a lot).
During normal running across switches and dirty track I do not notice any perceptible difference in speed and/or lighting brightness when hitting multiple small power drops in a row. I can watch the voltage on the module in real time and see it quickly drop and regain power over and over, and there is no effect on the locomotive or consist. However with a full and permanent power drop it seems that the locomotives drain the capacitors very quickly.
-Kevin