yes, the power connection on the V2 is a 4-pin XLR. anywhere in the 6-12V range will give equal performace, so don't worry about that. I think most people use 6V, simply because 6V batteries are generally lighter & smaller than 12 V batteries.
one thing that needs to be considered, however, is what the V2 is calibrated for. because it is bad for lead-acid batteries to be fully and completely disacharged, the units can be set for either 12V or 6V batteries. the setting is a cut-off voltage, below which, the unit will shut off, or won't even turn on. So, if you're V2 is calibrated for 12V, the cut-off voltage is probably somewhere around 10.5V (I'm not sure exactly where). so if you tried to use a 6V battery, the V2 wouldn't ever turn on. On the other hand, if your unit was calibrated for a 6V battery, the cut-off voltage is around 5V. then, when a 6V battery is losing power (and the voltage drops), the V2 would turn off to save the battery. You can use a 12V battery to power a unit calibrated for 6V, the only thing is that the V2 would never shut-off, because the low-voltage cut-off would never be reached, and you would be able to completely and fully discharge the battery. doing so would shorten the overall life-span of the battery.
the other thing to consider is that the V2 will be warm to the touch when using a 12V battery, because there is more energy to dissipate. however, it's not like the AD-1000, so that shouldn't be a big concern. just something to know about.
The V2 manual is here:
http://www.gracedesign.com/support/support.htmthat page also has instructions on how to calibrate the cut-off voltage for either a 12V battery or a 6V battery. and if you don't want to do it yourself, I'm sure you could send it in and they'd do it for you, if you need it done at all...
hope this helps.
- Jason