I have a bit of experience with those micro-helis, and first off you want to get either the Airhogs Havoc, or the Silverlit Picoo-Z. They are the exact same product, just marketed by two different companies. Don't buy a knock off, it's about the same as buying pirated pay-ware for FS, and the quality of a knock-off is often very poor.
With that out of the way- No, you couldn't replace the LiPo with a AAA. The voltage wouldn't be the same, and a AAA would be much heavier. They make them with built in LiPos because those are very light-weight and hold a lot power or run time for their size. The 8-10 minutes of flight that you get out of a Picoo-Z may not seem like much, but at this state of technology it's about the best that can be done for $30. But hey, you could always buy two or three of them to keep flying.
