How does an airbox work? Can I reshape it a little an have it function the same or is there a vortex or air flow pattern of some sort accuring inside of it?

I've turned my battery sideways and dropped it lower and would like to push it an inch or two into the airbox so that it is more hidden from view.

Small modification should be fine. People have managed to get these bikes running ok with K&N lunchbox filters and even pod filters. The airbox does increase the air velocity which is important for the CV carb to function but a slight modification shouldn't be much of a disruption. I would be prepared to make minor adjustments to the carbs.

I don't want to mess with the carbs.. do you think losing the space of approximately a large pack of cigarettes would change it so much that it would affect them?

Probably won't effect anything. But its hard to go backwards if it does.

From a technical standpoint, the airbox has a fixed volume of air which has a resonant behavior providing lower resistance to air movement at a certain frequency. This is known as a cavity resonance. If you reduce the volume, you will increase the resonant frequency. Practically speaking, you will just shift the torque peak higher in rpm by some small amount. You can test your change by just sticking a block or something inside the airbox to displace the same volume of air you intend to reduce by reshaping. I doubt such a small change will make a noticeable difference.

The cavity resonance also offers damping to higher frequency changes, which basically means it prevents peaky airflow or rapid changes in vacuum. This is why eliminating the airbox can make tuning a challenge, since transient pressure peaks and dips manifest as stumbles and misfires. Also the air filter element itself has an effect on airflow, but really only at high flow rates. That's why changing to a different drop in filter usually has no performance or tuning impact. You'd have to increase the bulk air demands to see any difference, which would mean higher revs or more displacement, more valves, etc.

Yeah scrap it, can't be f'd. Might hit it with the torch on the side to shift the petcock but not taking the amount a of space from it that I was considering.

I reshaped mine a little with a heat gun. Mostly to make the end that connects to the carbs actually flat so it would fit on the carbs correctly.

You can probably cut a section out and then fab up a patch if you need to. Not sure what kind of plastic it is, but one of those "plastic welder" kind of products (I think Permatex makes one) might work to attach some ABS to it and seal up your hole. Otherwise make your patch out of something like sheet metal, some scrap of stainless steel, etc., and pop rivet it in place, seal up with RTV.