Alternative WW2 scenario: South Africa joins Axis

[RF]

Suppose that in July 1940 the South African government of Smuts falls and is replaced by a government of Boer hardliners, who immediately sign an alliance with Hitler and declare war on Britain. South Africa seizes Southern Rhodesia (today known as Zimbabwe) and the colonial government there decides to join forces with the South Africans.
With South African and Southern Rhodesian forces now at war with Britain, both the KM and the RM are able to freely use South African bases. Operation Berlin culminates with the twins going to Simonstown instead of Brest, where they join forces with the Admiral Scheer, in preparation for a revised Rheinubung operation.

Would South Africa changing sides be decisive against Britain before both the USSR and USA are drawn into WW2?

And would Rheinubung be more succesful a proposition with the major surface ship threat in the South Atlantic?