Could Germany reach North Africa through Turkey and the Middle East?

Without Barbarossa, could Germany go through Turkey and the Middle East to attack North Africa?

The route faces serious supply problems: British forces would have warning, and German dependence on railways becomes a liability where the network runs out.

An advance through Turkey would still need a workable supply route into the Middle East. British forces already in Iraq would have intelligence and time to react, particularly before Japan began its own offensive. The British supply route to Asia was already going around Africa because of the fighting with Italy, so further trouble in the Middle East would not introduce that detour. German military logistics depended heavily on railways, whose reach became inadequate beyond Turkey. Highly refined railway practices inherited from the First World War could support some campaigns efficiently while leaving this proposed route impractical.