Hi Mikal,
Yes, you would be able to run the Galileo board using the step down regulator from Pololu and 4 D cell batteries in series.
If you use alkaline D cells (LR20) you will be able to run the board for maybe something like 24 hours, of course depending on battery brand, since the capacity varies a bit between them.
The math behind this is 12000 mAh / 550 mA ~ 24 h
The 12000 mAh is the capacity of the D cell and since they are connected in series, only the voltage is multiplied to 6 V, not the capacity. You might win a little bit in the down conversion to 5 V, but that won't be much... and the voltage might drop too much on the batteries before they are fully used which will shorten the time.
/Thomas
