If the Germans push through Turkey, even with Turkey as an ally, it means no Barbarossa, at least for a minimum of a year after OTL. It also means that the Germans are basically betting they will take the Middle East and this will force Britain out of the war. Just don't see the Germans doing this, even if the UK is out of the Middle East as long as they don't sign an armistice, some resources have to be directed against them - air forces, U-boats etc. The generals know that the USSR is getting stronger the longer they have before the Germans attack. Finally Hitler really, really wants the Lebensraum and thinks that the USSR will fold quickly, and that he can finish off the UK afterwards if need be. In the light of all that, the Turks would have to be crazy to join the Axis except at the last moment like Italy against France to see what they can get from the Soviet corpse.