Cap useless.
The battery in the rear is great, that means that the amplifier wont have to try to pull say 130 amps of current through the 20ft of 4awg as you mentioned. If your lead into the amplifier is only 3-4ft long, it shouldnt be as big of a deal.
Just know that the battery will not charge as fast, although I cant be certain you'll notice much of a difference with only 1500w rms, roughly, coming from it.
In sum, you should be fine.
Also - - - if nothing else, spend 20 bucks and buy yourself a digital volt meter, put it on the rear battery and watch it, just in case //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif