Minimal for average use. A multi-core CPU wouldn't really be utilized by most software but, if it can be done and keep the prices the same, apple will likely do it. Battery technologies are also improving. Most of the time little of that CPU would actually be used, however more graphically intensive games and things like that WOULD drain your battery quicker on a dual core chip, but not much.
I'm quite positive that Apple, if including a more-power-consuming processor, would compensate for larger batteries if the engineers deemed it necessary. They would stick with their 10 hour battery life, or go longer.
My only concern with these dual core CPU's is heat. I don't think apple would ever put a heatsink and fan on the iPad, doing so would negate a major function of the iPad in terms of portability. As processors get faster, they get hotter. For example, I remember when I built a PC (a long time ago, haha) with an Intel 286SX CPU, it has in big letters "Heat Sink Required" because it was the first intel chip to require a heat sink. It was very small and had no fan, however. Now, the i7's and AMD Phenom chips have big heat sinks with copper heat pipes and powerful fans, just to run at stock speeds. Technology has a come a long way, though, considering that 286SX was 33MHz and we run A4 processors at 1GHz(ish) without the need for a fan, just a small heat spreader. I just don't know if the technology is there to do the same with two cores.
They will definitely have to beef up the GPU to handle a higher res display, however. They may or may not increase the resolution, but if they do I don't think the A4 will cut it.