For any circuit to operate correctly, there must be a closed loop for current to flow. Therefore, current does flow through the return path (system ground, in your circuit).
Consider:
simulate this circuit – Schematic created using CircuitLab
As you can see, current flows around the entire circuit (dissipating most of its energy across the load) and eventually back to the negative terminal of the source (batteries in your circuit). So, you must consider the maximum current specifications of the pins, given the high currents in your circuit. All that current is definitely flowing in system ground.
If the current limit is 1A per pin, you should definitely include more pins to ensure reliable power delivery without overheating.
To further address your grounding concerns, I would recommend either purchasing a different connector with a higher amperage rating, or re-designing the PCB to have large and thick pads for connecting to the terminals of the battery.
Remember, all that current is flowing both from the positive pad terminal (+), through the circuit, and back to the negative terminal (-). Therefore, you must ensure the entire path along which the current flows has been designed to handle this current. If your traces are too long and/or thin, you risk wasting significant amounts of power along the delivery path. There's no such thing as an ideal wire, and having long, thin wires conducting large amounts of current is not good design!
Adding a few extra pins/pads for a localized negative (-) terminal for your battery will not cause any ground loop issues assuming your circuit was designed properly in the first place.
A 12 volt battery has 12 volts between its terminals. Voltage is always measured between two points - there is no "absolute" voltage.
If you have a 12 volt battery and an 11 volt battery, and connect the negative terminals, the voltage between the positive terminal of the 11 volt battery and the positive terminal of the 12 volt battery will be +1 volt, assuming the negative lead of your meter is on the positive terminal of the 11 volt battery.
If you connect the positive terminals instead, there will be a 1 volt difference between the negative terminals.
The term "Ground" is much misused in the electrical field. Occasionally it does mean a connection to the Earth, but most often it is just the point in a circuit that the designer chose to call "zero volts", and uses as a reference when measuring voltage elsewhere in the circuit.
Best Answer
Nope.
The entire body is conductive and wrapped in a tiny layer of plastic.
And: Fun part: With standard alkalines (thanks Nick) it's the + that wraps all the way round. At the negative you can actually make a small screwdriver glow by jabbing it in the tiny opening between the negative and the body. (THIS IS DANGEROUS! DON'T DO IT! ETC! But you could... :-D )
EDIT: Since you appended your question:
You could look into using conductive fabrics, but these are built up of normal fabric with conductive fibers inside, often metal. These fibers can creep into the gap between poles. You need to make sure of two things:
For the creeping problem you may be able to find plastic rings they use in building NiMH or NiCd battery packs to protect terminals from the wires running across. If you are going to be Alkaline, Zinc-Carbon (again, thanks Nick), NiMH, NiCd and Whatever chemistry compatible you need to protect on both ends.
To protect against sheath damage you need some non-conductive fabric or material otherwise in between, that actually wraps around, or this will be a problem at one time and you are not going to enjoy that.
End of EDIT
This is also something Dave Jones highlighted when he was tearing down these "battery booster clips". Next to the facts that many of the claims are exaggerated and/or bullshit, the entire metal clip is connected to the negative, which could cut into the plastic and short out your battery, which is a safety hazard.
That is beside the point of your question, but it's a fun little distraction when thinking about AA batteries, to have Dave explain all their properties to you:
Dave Jones about AA battery booster clip, if you're interested.