^ Seems strange for a transmission fault thought, no? Maybe not with all the electronics associated with them these days.
No!
Even my Lexus as far back as 98 used to go mental with low battery. Every warning light would light up. All of them. Our Audis also did the most bizarre things with weak battery.
Perhaps the mechatronics in the tranny might be sensitive to input voltages?
On some cars, if the voltage isn't correct, the system thinks the component is faulty/defective and behaves accordingly. Hence the warning lights.
Don't think this is EVERY car but have seen some really, really weird stuff (particularly with our Audis) when battery is low.