The voltage has nothing to do with the recycling time of the flash... the recycling time is due to how fast the capacitors can recharge back up (if you pump more voltage through it, they will simply burst or melt) and the actual flash bulb can take so much abuse b4 heating up to the max and burst.
The biggest problem everyone here is making is assuming that this is a simple circuit, it's not. The batteries are hooked to a flyback converter. This allows you to generate a large regulated voltage which charges a capacitor and sits across the flash tube. An ignition transformer then generates a spark at about 4000V which ionises the space in the flash tube. This changes the electrical properties in the tube and the bright flash is sustained by the voltage stored in the capacitor till either a timing circuit quenches this connection or the capacitor is discharged and the flash can no longer sustain.
Ok so that's the basics out of the way. A higher voltage CAN make the flash charge faster. In fact this is how the Nikon SB-800's additional battery works. It just boosts the voltage by 1.5V at the input to the flyback regulator allowing it to sustain a larger current in the inductors which transfer power to the high voltage side of the regulator. The risk you run is one of input compliance. Just because the SB-800 charges 1 second faster with 1.5V doesn't necessarily mean it can handle 3V or even higher without damaging some part of the regulator.
Also note the key word regulator. It regulates. Whatever you do to the input won't affect the output on any properly designed circuit. The flash charges to 300V regardless of the voltage on the input so there's no risk in damaging the flash bulb. There IS however a risk that you can overheat your bulb as the additional recycle speed means your flash doesn't have as much time to cool down between shots, and that can damage the bulb.
Cars don't run faster by using high octane gas, but you can increase the compression ratio of the engine with high octane gas which will generate more power. Your analogy is actually quite fitting here, and think of the regulator as a modern engine which will ramp back when the knock detection starts going off. Some cars just like some flashes actually do go faster simply by using higher octane gas.
In summary, don't do it without knowing the limits. Unlike your car analogy you can break your flash with a higher voltage. Find some concrete numbers unless you're a tinkerer who is comfortable with potentially having an expensive paperweight. Oh and 12V will almost definitely be too high.