no do not use a battery! you only use batteries to test phase. if you hook it on the wrong wires you can cause serious damage or injury.
Here's the info I have for a 2012. should be the same for 13, but there is a chance its not.
Battery BROWN/RED (+) RADIO, PIN 1 OF 24 PIN PLUG
Ground BLACK (-) RADIO, PIN 13 OF 24 PIN PLUG
Illumination BROWN (WITHOUT SYNC) (+) RADIO CONTROLS, PIN 3 OF 8 PIN PLUG
Power Antenna YELLOW/ORANGE (+) RADIO, PIN 2 OF 24 PIN PLUG
Amp Turn On YELLOW/PURPLE (+) RADIO, PIN 18 OF 26 PIN BLACK PLUG
LF Speaker (+) WHITE
LF Speaker (-) WHITE/BROWN
RF Speaker (+) WHITE/PURPLE
RF Speaker (-) WHITE/ORANGE
LR Speaker (+) WHITE/GREEN OR BROWN/GREEN
LR Speaker (-) BROWN/YELLOW
RR Speaker (+) BROWN/WHITE
RR Speaker (-) BROWN/BLUE
Amp Location RIGHT SIDE OF CARGO COMPARTMENT
edit: btw, you're not gonna damage anything by having the polarity reversed (out of phase), it just won't sound quite right. you will also need to hook it to the left speaker as well to make sure you are getting all the sound just in case something only plays bass from one side and not both.
2010 Volvo C70
2011 Harley FLHTK
Midwest Crew #22