I can put an AM radio next to the usually poorly snubbed diodes of a big linear amplifier and hear things too, and usually much larger current spikes at 100/120Hz on the AC line.
I would be far far more concerned about the power quality on the DC end of a wall-wart that is highly unlikely to be designed for optimum noise rejection for audio equipment than radiated EMI or what goes back on the AC line, which at least, if you buy approved stuff, has to meet some standard.
I would be far far more concerned about the power quality on the DC end of a wall-wart that is highly unlikely to be designed for optimum noise rejection for audio equipment than radiated EMI or what goes back on the AC line, which at least, if you buy approved stuff, has to meet some standard.