Amps do have caps inside of them and they're probably used to stabailze power. But, the manufacturer assumes you have a stable power source in the first place. If you give the amp a source with a relatively large AC component (2V P-P), I don't care how good your amp is, it won't be able to stabalize that. A large external capacitor will apply an initial load to the system, technically, it will always be a load on the system. But, once the cap is charged, it will discharge quickly to help stabalize some of he AC components on your power line.
All in all, if you want to do it right, definately upgrade your car's wiring. Also get a cap, 1-5F should be fine. Get a better alternator, get a better battery. It's just like an engine, you can put a blower on it, but you'll need to buy a billion other things to keep it running!