1st, does the sound system pull it's energy from the traction battery or the 12 volt? 2nd, what amount of amps is it pulling? Obviously no where near the number the AC is but is it possible it's pulling a couple amps at a pretty loud volume? Note to mods: I didn't put this in the electronics sub because of it's possible, albeit it VERY small, impact of FE
Well I don't know how much it uses. But everything has has a adverse effect on your fuel economy. The 12 V is charged by traction battery and the traction battery is charged by regen breaking and coasting etc.
It's almost certainly negligible. Most parts of the head unit are probably powered on regardless of whether you're listening to music or not. At reasonable volume levels, power consumed by the speakers is probably pretty low: I have a 500W RMS 5.1 speaker system on my computer. I was curious how much power it was drawing when listening to music at normal levels, so I got a Watts Up meter from the library to measure it - any time it was on, whether playing music or not, it was at about 20W. The extra power to drive the speakers was minimal at normal volume levels. It takes double the power to get a 3dB increase in loudness, so if you decrease the loudness by 20dB, you're only using 1% of the total power you could be using. Since most people don't have their volume turned up all the way (or if they do, the music source they're playing isn't all that loud), I think most of the time the sound system will be drawing a tiny fraction of what it is rated for. As a confirmation, you could look at a ScanGauge, but I'm certain that you can't tell the difference in HV battery amps between radio on and radio off. It's typically 1.0-1.5A while stopped (and the battery voltage is probably 230V or something - something a little over the nominal 201.6V, anyway - giving 230-345 Watts for the whole car, including brake lamps, dozens of computers, etc). I bet that bobbing your head with the music while trying to get a no-arrows glide has a bigger effect on your fuel economy, as your foot wiggles a bit from the head bobbing.
I would assume it's pretty negligible as well but for those that listen to it very loud with the lower end all the way up it could be a small FE hit. Bass does take more energy than treble for the same dB, correct? And I would also agree that for some music can have a distracting effect that can limit some hypermiling techniques. However, for others it may keep them more calm allowing them to drive more efficiently.
Yes, the sound system does use electricity, which theoretically hurts the mpg, but I doubt anyone could measure the difference. There are too many other variables involved. The driver's hypermiling technique is often the biggest variable. Bass does require more amplifier power than treble, since it's moving a larger speaker over longer distances. However, I also have a 2012 Prius II, and it doesn't have significant bass output in volume or depth. The midrange probably draws equal or greater power than the bass. Also, the stock system uses high sensitivity speakers designed to draw less amplifier power.