Our experience with ESP8266s is mixed. My colleague Brian (@borpin) recommends a Raspberry Pi Zero W instead - more reliable, he says.
The reason for asking about the power was because of the battery shunt. As the Arduino power will probably be common to one side of that battery one way or another (unless your converter is completely isolated on the input side - which conflicts with your 12 d.c. inputs) then depending on which pole of the battery the shunt is in relative to the common, you could have an isolation problem with the millivolt shunt input.