I doubt if Hitler would have fought Japan for purely logistical reasons. It's a long way from German and Japanese territory. The closest they could link up would have been via the Middle East and India. The distances to travel from Germany to Japan through other means, like Russia or China, would probably have been prohibitively long. Add in the facts that one needed a strong naval force to defeat Japan, which was something that Hitler was sorely lacking outside of U-boats, and that a victorious Luftwaffe would have been evenly, if not outmatched, by victorious Japanese Army and Naval Air Forces, than it would have been a far too difficult and uncertain task to fight Japan. Just my opinion!