Find out for yourself. In your Android device’s Settings, choose Battery, then scan the list of applications that have been using your battery since your last charge. If you have a particular live wallpaper installed, it may show up by name in that list, or you may see your live wallpaper’s impact in Display. You could install an app like System Tuner to see exactly where your system is spending its resources, but a casual perusal of your phone’s Battery list should show if there’s a notable disparity between your wallpaper or Display and everything else.
Live wallpapers don’t draw a lot of power if they are well crafted, if you don’t spend a lot of time on your home screen, and if you set your screen to shut off fairly soon after you stop interacting with it. All that noted, however, live wallpapers are a good place to start if you want to cut back on potential energy drains.