Any conductive object can be an antenna. However, effective antennas are approximately 1/4 the wavelength of the radio signal being transmitted, or 1/2 the wavelength for a dipole antenna. Headphone wires, approximately 2m in length, could be effective antennas for 40 MHz or 80 MHz radio signals. (80 MHz, you'll note, is close to the 87.5 MHz-108.0 MHz FM radio bands, which might give you a clue why some phones with built-in FM receivers require the headphones to be plugged in).

However, music has frequencies in the range of a few dozen hertz to a few kHz, which is in the "ELF" and "VLF" extremely or very low frequency bands. Some communication occurs at these frequencies, but it requires high-power transmitters with antenna arrays that are massive civil engineering projects tens of kilometers long rather than 2m long. These transmit to submarines towing long wires at small, inefficient fractions of the target wavelength, because these frequencies can penetrate saltwater.

Also, the headphone cables are not a single wire, they're a pair a pair of wires, each side carrying both a signal and the return or ground loop.

You might be able to inductively couple to this loop, like you would inadvertently if you're running unshielded, separated speaker wires near unshielded, separated 60 Hz power cables with poor grounding - but at that point when you're running the receiver wire a few millimeters away from the target's headphone cable, I think they'll notice and object to your tracking attempts...

Yes, well I remember the stories of EMI-certified equipment radiating information that was being received by CIA agents in a van parked outside the building.

https://en.wikipedia.org/wiki/Van_Eck_phreaking

Van Eck phreaking relies on detecting radio waves produced by equipment like a CRT operating at tens of megahertz, a high-power VRM operating at 500 kHz, or frequency shifts in a processor clock operating at a few GHz. These wavelengths can be radiated by antennas of reasonable size. If someone was able to pick up radio waves off a headphone cable, it would probably be from the higher-order harmonics produced by switching power supplies in the amplifiers, not from the sound waves themselves.

Also, EMI certification just means that it doesn't generate interference that will damage other equipment and that it's not permanently damaged by external interference. It doesn't mean that it doesn't radiate any energy at all. FCC limits are pretty noisy when you're considering whether or not you can detect emissions with an active antenna.

I have a phone that has a FM radio, but it only works if headphones are plugged in (whether or not you tell it to have sound coming out of them or the speaker)--it uses the headphone wire as an antenna!

Humans are antennas too, you can be tracked through WiFi. https://cs.nju.edu.cn/ww/papers/ubicomp16_gait.pdf

I always remember back to one of my electronics labs in college. We were trying to debug a circuit from which we could get no readings. The oscilloscope, with no working leads, was sensitive enough to detect our movements a few feet away from it...

Or more simply, track the actual phone if it doesn't have all it's radios off.

That's why phones have got MAC address randomization.