I would guess the motor is only going to draw the current it needs and for which it is rated to draw. You may get longer spray time but you will not overdrive the pump for increased performance.
Correct. Voltage is like water pressure, current is like the available volume of water. Just like a pump, an electrical device draws current (amps) from the supply (battery). As such, a normally functioning electrical device can not draw more current than it can handle when the supply is at the correct voltage (pressure).
However, if you DOUBLE the rated pressure (12v -> 24V), you can overdrive the pump ultimately resulting in it's catastrophic failure.
A series connection would increase the output right up until the time you burnt out the motor. (probably ten seconds or so)
Actually, it could be a whole lot longer than that, but the results would be the same. Electric motors fail because heat melts the insulation on the wiring causing a short circuit, which causes a huge increase in heat, and so on until you have a smoking mess.
What's not often told is that electrical resistance increases with RPM, thus decreasing the current in the coils and the amount of heat generated. So unless you significantly overvoltage a pump, it probably won't fail because of the voltage. What will happen is it will spin a hell of a lot faster and the bearings (or the pump head) will overheat from excessive RPM's and seize. or fail outright from added stress.
The point is that it may work fine at 24v for "a while". Unfortunately, "a while" may be ten minutes or ten days. But ultimately running a pump at 2x rated voltage is a bad plan because you have more than just the motor to consider. Can the pump handle 2x the RPM? 2x the flow? Can the internal valves handle 2x the pressure? Can the hose/clamps? the pressure switch?
You can however, run two pumps in parallel at 12V each to double your volume. But unless you increase your orifice size, you will double your pressure. Make sure all components can handle the higher pressure or adjust your orifice accordingly.
It is possible to increase the voltage on some motors without destroying them immediately. For example, a lot of people convert 12 volt power wheel systems over to 18 volt to get more power, but it still shortens the life of the motor.
There is a great example of what I just described. A 50% overvoltage works in this case without immediate failure. Will it work for you? Only one way to find out....