Powering a raspberry Pi using an ESC (Electronic Speed Controller)
You need to ensure 5V @ 700mA according to the manufacturer.

And, Yes, you can power Raspi from batteries.

From Raspberry PI Faqs

Can I run power Raspberry Pi from batteries as well as from a wall socket?

Yes. The device should run off 4 x AA rechargeable cells, but there may be stability issues as the batteries lose their charge.  Using 4 x AA Alkaline cells will result in 6v and it is therefore recommended to use a voltage regulator.

You could use this example too, that power with 3V3 and use a batteries.