Would Hitler have conquered Russia after the battle of Kursk if the US had not invaded Italy?

I saw on the National Geographic that the Germans were on the brink of victory in Kursk in 1943, and where going to finally seize Russia. But at the most crucial moment of the battle the US invaded Sicily and Hitler ordered half the troops and tanks to leave Kursk for Italy. And this turned the battle around catastrophically for the Germans and started the unstoppable Soviet march towards Berlin.