It depends a lot on what the system is built like. Old points ignition systems had a capacitor that charged up as the points were open and when the points closed the capacitor (called condenser in those days) discharged through the coil, pulsing the coil primary inducing the current into the coil secondary causing the high voltage spark. If the points and capacitor w ere on the ground side of the coil, the inductance and resistance of the primary winding could be enough to keep the capacitor from charging up as high as if it were on the positive side of the coil. I have not looked at newer systems enough to guess if the same principle applies or not, but a coil is not a polarized device by itself, but supporting parts may be.
A car coil is actually a transformer, two separate windings, primary (low voltage in this case) and secondary (high voltage in this case). The transformer can be wired as a step up or step down, depending on the need.
If you tried to apply the low voltage into the high voltage secondary, then you would get very low voltage out of the coil primary and not have enough voltage to ever jump the gap on a plug. An older ignition system would have about 20,000 volts out of the coil secondary and if you pulsed the 12 VDC to the high voltage side of the coil, the output on the low voltage side would be very low, in the .0075 VDC range.

Danny