A discharged capacitor has zero ohms resistance. Hooking it directly to the battery is like putting a screwdriver across the bat terminals. You get sparks and you weld the wire to the cap terminals. Best case you blow the fuse, worst case you damage the cap. The amplifiers aren't affected.
Also, if you remove your battery for any length of time or if it goes dead, the cap will discharge. You can charge it by putting ANY 12 volt light bulb between the battery pos terminal and the pos cable. When the light goes out the cap is charged and it's safe to hook the cable to the battery. The bigger wattage the bulb is, the faster the cap will charge.
The time constant to charge a capacitor to 63% of the supplied voltage is R*C. It takes 5 time constants to reach full charge. So a 10 ohm resistor (or bulb) in series with a 1 Farad cap takes 10 seconds X 5 to reach full charge.