It will use more battery in the same way as carrying around a small bottle of water in your car will increase the fuel consumption due to the extra weight.
The amount of energy used by the RAM is negligible compared to the major heavy lifters in the laptop - the screen, the CPU and the GPU (assuming one is fitted). These things dwarf everything else inside the machine in terms of power draw. The next closest things I would wager would be the SSD during writes, and the USB controller if you have something plugged in that requires a lot of juice (like charging an iPad or similar).