There's very good reason to think it won't happen. This [1] paper from the UN provides a good overview of South Africa's extremely unique situation. Similar information is available here [2]. The gist of it is that South Africa's declining fertility rate was exclusively the result of extensive efforts, not entirely benevolently motivated, by their former [apartheid] government.

[1] - https://www.un.org/esa/population/publications/completingfer...

[2] - https://sarpn.org/documents/d0000104/page2.php