I decided to rephrase the original question. I appreciate the time some people took to make replies, but the replies has nothing to do with the question specifically asked in the title of the thread. Again if someone could answer that for me, please enlighten me. I probably should have mentioned I do have the Big 3 Upgrade wiring (0 Gauge) properly installed by myself. It definitely helped with not only the car audio but all accessories (headlights/dashboard lights etc). Besides headlight dimming, at what point do other drawbacks come into play if the amp draws too much power from the battery. Will the car shut off, can it damage the alternator, damage the battery, meltdowns etc. Thanks for any feedback on this specific question! I know my amp and battery need to be upgraded, that's not my question though.
Let's venture into speculation. I do not know the specifics of your alternator or battery. The alt. is there to provide x amount of amperage through a regulated x amount of voltage to a storage device, ie; Battery. This battery is designed to be charged and release an x amount of amps over a x amount of time, with a reserve for sudden release.
The manufacturer designs an allowance in the alternators output ability. Lets' say for example 25% for "accessories".
Suppose the VW alt produces 100 amps at highway speed. Your cars electrical at night with headlights, phone charger, GPS stuck to the windshield, etc. is using a continuous 75 amps. The equipment in the car is requiring the battery to discharge this amperage at a rate lower than the alternator is supplying, thus maintaining a continuous stable flow of electricity.
Now put a amplifier in the mix that is capable of drawing 50 amps of current on a heavy bass note at full tilt...as you turn up the volume, you notice the headlights dimming with the beat, especially those long, heavy bass parts of the song...the headlights are dimming is your cars battery amperage is being drawn down quicker than it is being supplied at a rate beyond what it is designed to release. As the electrical system destabilizes, the components are trying to work doubletime to maintain a stable voltage supplying the amperage (Current). When the voltage drops below the amplifiers design specs, the amp can fail..quickly. There is alot more to research in an amplifier than just wattages or thd's...and the cheapest power for the $$ can cost more than you bargain for. Kenwood makes good stereos though.
The big 3 is to help ensure each component has sufficient wiring to ensure current flow. The weakest link in OEM electrical systems is the wiring itself. I have burned wires, as a lesson (ps FUSE the ALt to Batt+ wire!). I have replaced many OEM sized lead acid batteries due to internal plate failure. The big wires and a $200 battery suitable to the required amperage throughput will save money vs fried electrical and a new $80 every few months for a battery replacement still not suitable for the job..
The AGM Battery I posted earlier was an example, as stated.(I prefer Kinetic) There are cheaper, there are more expensive. It is recommended to talk to the battery manufacturer and discuss the system design and vehicle fit before any AGM purchase.
I am sure I might have missed something, or maybe a misused term here or there....but perhaps some of the more knowledgeable and experienced can add to this thread