Can you reduce audio noise by decreasing input impedance with a resistive load?
Three possibilities here:


Random electron-movement noise: a 10,000 ohm resistor in 10,000 Hertz bandwidth, ignoring any A_weighted responses, will provide 12 nanoVoltRMS * sqrt(10,000 Hz) == 1.2 microVolts RMS noise; whereas a 62 ohm resistor will provide 100 nanoVolts RMS.
your wiring may pick up RFI of AM, FM TV, cellphone energy and the powered-speakers have opamp inputs that non-linearly respond to that RFI/EMI and rectify it and downconvert it to within audio range and you hear that; cure is better cables, or RFI filters added at inputs to the powered-speaker.
As mentioned, powered systems almost always have switch-mode power supplies for efficiency and low heat generation, but the switch-mode transformers still have primary and secondary windings with some capacitance between the two windings. The energy coupled between those windings will, per the assistance of mother nature, explore ALL possible paths back to the high dV/dT switching transistors in the supply; one of those paths will be your cable into the speaker.