That goes without saying.
They don't say what the 'AC voltage' is, it must be pretty high
[or sucks a lot of milliamps], as the biggest Xformers can pull up to 750 mA if you have enough LightSheet/Rope attached.
At 9 Volts, that a few watts.

The AC induced noise could get worse if you made it pulse on and off with the sound. If its was lit stedily it would be less of a problem I think.