VASAX:
http://chdk.wikia.com/wiki/Camera_Power_Consumption
Q. Does the CHDK program consume additional battery power?
A1. (wise guy answer) Yes, because you will use your camera more often!
A2. The dreaded and mysterious battery-drain issue. You'll find out that not only does your camera get warmer, but that your batteries drain 10x's as fast at first. Fear not, this has nothing to do with CHDK itself. It has to do with how much you are trying to make your camera do things which you've never done before. 10+ shot bracketing sequences, intervalometer tests, checking out all the scripts, taking hours to find your favorite colors for all the features, tweaking your OSD (screen) layout, comparing histogram types, setting/testing Zebra mode sensitivities, loading all the Grid files and trying to decide on a favorite, testing the file reader on a favorite e-book, getting lost in Sokoban or Reversi, etc., etc. Not being able to put the camera down for many hours during your exploring and making it do new things. You may claim that this happened after only for 10 minutes of using CHDK, but I think if you really timed this you'll find out you've been at it for hours. (Time flies when you're having fun.) There is also a psychological effect with having that battery meter. NiMH batteries quickly drop down from their topped-off voltage to a more average base voltage during use. You see this quick drop in the meter after first using fresh batteries and think it is always dropping that fast. This "CHDK is a huge battery drain" effect/perception wears off after about 3 months of playing with and familiarizing yourself with CHDK, You might want to consider 2 more sets of rechargeable batteries (always keeping 2 other sets topped-off, a high-speed charger might help) until this issue has resolved itself. :)
B. Some people measured the battery consumption rate and found that using the CHDK does not affect battery consumption (either not at all, or just minimally). It makes no difference whether the live histogram etc. is activated or not, because the CPU of the camera is always running (looking for keyboard presses in the loop) and the histogram is calculated even if it is not displayed.
CHDK users also tend to half-press the shoot button more often than regular users, as this allows them to see not only the green/yellow rectangle, but also the histogram, zebra, etc. Keeping in mind that this also is constantly engaging auto-focus and other more power-hungry camera functions more often.