Clever Allied codebreaking and code talking certainly helped the Allies win the war. Both the German and Japanese military codes were broken early on, with the result that the Allies generally knew in advance almost every move the Germans and Japanese were going to make on the battlefield. This led to many Allied victories, the Battle of Midway probably being the most decisive of them.

It was the British who broke the German Enigma code by capturing vital code equipment and info off a German U-boat. (This was recently retold in an American film to make it look like the Americans did it...) American codebreakers broke the Japanese code and had early warning of the impending attack on Midway Island, enabling a much weaker US fleet to ambush and destroy 4 of Japan's 6 largest aircraft carriers...a master stroke that turned the tide of war in the Pacific.

Using Native American codetalkers was a smart ploy...it must have given the Japanese fits! ;-)

I think that the Allies would have won the war anyway, even if none of the above had happened...but they wouldn't have won it nearly as soon, and their losses would have been far greater.

The Germans and Japanese were naturally trying to break Allied codes all through the war as well. To what extent they succeeded, I don't know. You don't hear much about it. I would gather, though, that their efforts were largely unsuccessful.