Absolutely. Throughout the twentieth century, many Europeans living elsewhere in Africa moved to South Africa when their country/territory of residence became independent of European colonial rule.

Some Europeans even migrated multiple times for this reason: e.g. a European in Kenya moving to former Rhodesia (now Zimbabwe) upon Kenyan independence, and then moving again to South Africa upon independence/majority rule in Zimbabwe. Zimbabwe was an especially major source of White emigration to South Africa on account of its large European population that, in large part, shared South African attitudes on race.

As for white immigration to South Africa from other continents, it definitely took place but I don't know enough to give you an idea of its scale, especially because "motive" for migration is difficult confidently determine.