I'm an EE by degree (not trade) and I've been thinking about this. The choke cores (as they are referred to) work by blocking EMI and RF that is traveling 'along' the cable.
Would it hurt in my opinion, no. Would it help? Maybe.
This question is sort of like 'should I use Marvels Mystery Oil in my car'. Will it hurt, no. Will it help, who knows, no one has ever shown either way.
Considering the very low frequencies (up to 22khz) that you are using for audio (remember, that's in the basement of the frequency band) and that these cores are designed to trap stuff in the EMI and RF, MHZ range) I can't see where filtering out anything other than an AM radio station that happens to have it's transmitting antenna in your back yard!
But on the other hand, if those speakers are powered speakers that may have integrated sub-woofers there could be an application. The power supplies in those speakers are specifically designed to not couple any EMI to the audio, but that's not saying that the amps could not be amplifying any junk coming into then via the speaker wire or LFE channel. In that specific case, I think you might get something by adding a core or two.
The nice thing is that these puppies are dirt cheap (about $2 at Radio Shack) and are generally stuffed in about every high end piece of audio gear anyway, but for a good reason there. Try not using the core on my Samsung 63" PN590 Plasma TV and you can literally see the difference right on the screen!
Oh and yes, the core should be placed in one of two positions. As close to any equipment that might be creating EMI/RF to choke it at the source or as close to the input of anything taking input to choke off anything traveling on the wire.
So in power cords, right at the entry to the gear. Chokes anything coming in and anything coming out.
For USB, line level, etc, the choke should be at the device (hard drive, LL input) to clean the signal before it gets used.
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