I have a slightly more elaborate sound system upgrade in our Plug-In Prius, which has a tiny 12 volt battery, just like the i3:
The 12 volt system is more than adequate to power the 500 watt subwoofer amp and 4 X 100 watt sound channels. I power the system directly from the battery, with its own inline fuse. Power sensing comes from the car's original sound system output to the JBL MS-8, which completely powers down the system when the car is turned off.
Folks tend to not make a distinction between power potential, and power actually used. While the system is capable of outputting as much as 900 watts, I've taken measurements at a sound pressure level louder than I would ever consider listening and found a peak of about 70 watts, and an average less than 20 watts - no strain whatsoever on the 12 volt system.
By the way, that works out to a potential impact on range of no more than 1/10th of 1 percent, or about 143 yards per hour of the i3's 81 mile range, and then only at a continuous, painfully loud listening volume. At normal volume levels, probably closer to 15 yards per hour or so.