Paul (Brennan employee) has said elsewhere that a B2 *can* run on 12VDC, in cases where one might want to use it in a car or boat -- I think the only obvious impact is that the amplifier won't play as loudly as it can on 24V. You've said that you don't intend to use the internal amp, so that should not be an issue. Don't go any lower than 12V, though. (And don't go any higher than 24V.)
I know that, with AC supplies, lowering the voltage often increases the current requirement. I'm not enough of an engineer to know if that's also going to be true with a DC supply.