This rather depends on your perspective of what the word "effective" means.
Those US navy bombes are for Kriegsmarine "M4" Enigma, which didn't even exist when Bletchley Park began breaking Enigma. They came on line in mid-1943. So, by this point the Axis is defeated in Africa, and Barbarossa is failing, the German Army is in trouble on the Eastern Front, it has faced some big military defeats there and cannot continue to sustain these losses, but Russia hardly seems likely to accept a peace deal after being betrayed previously.
Now, the war wasn't _over_ in 1943 even in Europe. But there had been three years of code-breaking (including of Enigma) at Bletchley by that point. It's true that Huts attacking M4 sent data across the Atlantic to the US navy, but again, that's from mid-1943, prior to that the British were using their slower machines because you can't win wars by waiting until you have better equipment.