No, the Chromecast does not have a battery, but is connected to the power supply with a microUSB cable (5V/1A; adapter/"charger" is included). However, since the power consumption is rather low, you can also operate it via battery or, for example, if your radio has a USB port, plug it in there [1].
Since you ask whether the Chromecast has a battery, I would like to make this comment (I assume you are aware of this, but better safe than sorry): the Chromecast must be on the WLAN [2] for it to work. That means it's not a portable speaker like a Logitech UE Boom or JBL Flip.
Since you write "12 volts" - do you want to use it in the car? I've never tried it (I use Bluetooth or AUX), but I'd be curious to know if (and how) it works!
1] e.g. with this [TechniSat Digit CD (Anthracite, DAB+, USB Host, CD) - very practical!
[2] Ethernet also works, see
https://store.google.com/product...
