No, AppleCare will not cover a battery, unless it is defective.
b. Limitations. The Plan does not cover:
(ix) Consumable parts, such as batteries, except in respect of battery coverage under APP for iPod or unless failure has occurred due to a defect in materials and workmanship;
All batteries lose capacity over time. This Apple doesn't cover. However, if your battery suddenly fails to hold a charge at all, or causes your computer to crash repeatedly, Apple will replace it.
That is what happened to my battery. Just after two years my battery started to slightly bulge and dropped from holding a charge 2+ hours to being able to run for about 5-10 minutes. So the genius bar replaced it under my applecare at that point.