Batteries only store energy, they do not create it. The alternator is what creates energy for your charging system. If your drain exceeds the amount of energy created.... well it doesn't take a nuclear physicist to see what would happen.
Time adds a complexity to the story however. Average power drain over time, and average power creation over time. For example, your stereo does not draw a constant amount of power, it fluctuates according to the material being played (unless you run pure class A amplifiers, which you dont).
People tend to think of power consumption, and power creation, in a 'snapshot' of time, at any given moment. Your stereo may drain grossly more current for brief moments than your alternator may provide, this is where your storage capacity comes into the picture.
As said above, your stereo may draw larger amounts of current from your charging system than the alternator can provide at that moment. The battery will absorb those peaks in demand, allowing the alternator to catch up when the demand decreases (bass note diminishes). But if your demand over time exceeds whats your charging system creates over time by too much or too long, your storage capacity will be depleted.
How much current draw your system requires over time is not only affected by the size of your amplifiers, but also by your listening habits. Do you listen at full blast every time you are in the car and the engine is running? Or are there times when the alt will see less demand and have more time to catch up? This is dictated by nothing we can guess at here, only by the owner/listener's discretion and taste.
All this background info to answer the question, will adding batteries help...? Who knows. Depends on too many variables, many of which we cannot control or predict. If your charging system is close to adequate, adding another batt may be sufficient to keep your car starting every morning. But it wont help keep voltage up when you are running down the road late at night with the A/C on, your head lights, and are cranking the music as loud as you can to try to impress your girl. And if your charging system is not close to adequate, adding more batts will simply delay the inevitable... needing a jump start.
Trying to acheive your 'real tested proof' would involve a long and complicated testing procedure that, in the end, would cause more arguements than solve. If you understand whats happening within a vehicle's charging system, said test is not necessary.
