We have no need for expensive power cords or line conditioners because we got a battery! But if the battery is charged with dirty power, doesn't it stand to reason that the battery then becomes contaminated? If that is incorrect, what happens to the dirt? 
Wind Chaser,
Think of a battery as a water container, and the battery charging as water. It doesn't matter if you fill it up with a smooth and continuous flow of water or if you fill it up sporadically with big and little splashes. Once that water container is filled up, it is very stable. The battery is an energy storage device, just as the water container stores the water. All the fluctuatons (noise, or "dirt") is absorbed by the battery, which then outputs a very direct current (DC).
If you do a seach in google for something like "battery charging," I'm sure it can be explained a lot better than this...
Regards,
