I am not so sure. China has been developing through Africa for the last 30 years, which I suspect is a way to deal with these kinds of problems. They have issues there with building healthcare and skills, but it is similar to what has happened in China over the last 60 years.
However, pretty much all countries are going to have issues with this and there ae only so many skilled immigrants to go around. This means that the countries that "pick first" and integrate well will have an advantage. The nationalist parties that are slowing immigration and integration are shooting themselves in the foot.
Globalization like China's activities in Africa depend on resources China does not currently possess like a blue water navy formidable enough to secure its lines of communication absolutely vital to it. All globalization including China's is possible due to US tax payers footing the bill for this Cold War arrangement where the US guarantees safe seaways for the capitalists and participants of Bretton woods. This system has been on the decline since the 1990s. Trump and Biden are both been investing less in global security than their predecessors.
The continents are likely to become less connected going forward.
Also, I find it unlikely that the Chinese would open to hundreds of millions of young Africans immigrants to replace their children.
They don't have to. They are setting up schools, hospitals and training in Africa. They plan on moving a lot of their production there I assume, which is what the west did with China.
If that's their plan how to achieve geopolitical dominance, I'd say it could become difficult to implement. Energy from the Middle East, production in Africa, and consumption in China. No blue water supremacy and surrounded by a chain of major islands inhabited by people deeply suspicious of them or by traditional enemies.