Originally Posted by JimBlake
Normally the battery doesn't supply any of the power while the engine's running. The alternator does that. But if you unhook the battery, the alternator can make some voltage spikes that might fry your ECU.
Very true. The battery acts as a buffer to absorb some of the voltage coming from the alternator. Alternator voltage is around 14 volts and everything in your car runs off a 12.6 volt battery, so the battery will absorb some of that power and distribute it without the voltage spikes.