Relevant: IS MODIFIED OR TAMPERED WITHTHIS WARRANTY SHALL NOT APPLY IF THIS PRODUCT: (a) IS USED WITH PRODUCTS NOT SOLD OR LICENSED BY NINTENDO (INCLUDING, BUT NOT LIMITED TO, NON-LICENSED GAME ENHANCEMENT AND COPIER DEVICES, ADAPTERS, AND POWER SUPPLIES); (b) IS USED FOR COMMERCIAL PURPOSES (INCLUDING RENTAL); (c) IS MODIFIED OR TAMPERED WITH; (d) IS DAMAGED BY NEGLIGENCE, ACCIDENT, UNREASONABLE USE, OR BY OTHER CAUSES UNRELATED TO DEFECTIVE MATERIALS OR WORKMANSHIP; OR (e) HAS HAD THE SERIAL NUMBER ALTERED, DEFACED OR REMOVED.
Like with all electronic devices, your warranty is voided should you open it up. These are not PC's where each individual component falls under its own warranty, it is considered a whole.
Edit: I never actually noticed the part in the manual about the battery cover. However, it does say not to remove it unless directed to do so by Nintendo support. You could be on the edge here regarding no trouble with your warranty and it may tip one way or the other.