They may be referring to how long your power wire is and the amp draw of the Kicker. You can start a fire if your power wire isn't big enough to support the current being pulled through it so it'll heat up. Get's hot enough, it can melt the outer jacket and arc against the body of the car. That being said, if your using quality 4 gauge, it's not 100 feet long, and it's fused, it's pretty unlikely to happen.
as for the battery, it depends on your car's stock alternator, how old/big the battery under the hood is, and how many amps that Kicker is drawing from your stock electrical system.
The first thing I'd do, is get a voltmeter or at least a DMM to monitor your voltage at the amp so you can determine if your car's stock electrical system can keep up with the amp's draw. If it tanks the voltage every time the bass hits, you may want to consider throwing in a small AGM for support, or just replace the starter battery with a bigger AGM if you have the room.
on 1000 watts, I doubt you'll be able to hear the difference in loudness.