To answer your question, no. If your power wires are choking your amp it will not produce as much power, and not draw as much current, which in turn will not cause as significant a voltage sag in your charging system which will lead to less dimming.
Most everyone with 1000w or more deals with some degree of dimming. It's up to you when it crosses the threshold of being a problem. At that point it is probably time to consider an alternator upgrade.