Even if the screens are earthed, if the power supply fails mains could be present on the internal circuitry, which would extend to the tip of the 3.5mm plug going into the i-device.
So the options would seem to be:
verify the amplifier has appropriate isolation built in;
use an appropriate isolating transformer on the audio input;
supply the amplifier from an apporpriate isolating transformer (like a shaver supply unit, but that won't be powerful enough);
just wire it up anyway as it'll probably not kill anyone.
I can't recommend the last but it's what I've done in my bathroom.
So the options would seem to be:
verify the amplifier has appropriate isolation built in;
use an appropriate isolating transformer on the audio input;
supply the amplifier from an apporpriate isolating transformer (like a shaver supply unit, but that won't be powerful enough);
just wire it up anyway as it'll probably not kill anyone.
I can't recommend the last but it's what I've done in my bathroom.