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You could use it if you had another one with a female headphone jack. You could play your music to a speaker in another room if you have Ethernet in both rooms. Copper is copper.
I've done this. I've made speaker wire to ethernet adaptors to connect speakers in a different room through the walls to an amp. Feels and probably is so wrong.
It really depends how much power you put through the cable, ethernet is something like 0.2 mm2 per core. You'd definitely want to double up cores.
While, as you said, both wires will conduct electricity just fine, they will have different AC impedance.
I would guess this wouldn't make much of a difference if you go Audio->Ethernet->Audio, since sound is at fairly low frequencies. But Ethernet->Audio->Ethernet might have problems with really high data rates, like GiB/s.
Hell, 10/100base-t only uses four wires so you could run internet through a 4-pole 3.5; though YMMV depending on the particular 3.5mm's specs. I don't know if drivers would be a problem, but perhaps a 4-pole 3.5 to USB would be handy.