No, if your population had 1000 births but 1000 deaths in a given period of time, you are not experiencing population growth.
If you have positive population growth, it isn't because your population is experiencing a negative rate of deaths.
The ugly fact is that in low food conditions, more people die faster. This is not good for population growth.
And yet population growth still happens. As I noted, birth rate goes up too and there are plenty of examples of places over the past century that had low food supply yet still had high population growth rates. It's only when a society transitions to not enough food per person to keep everyone alive (which incidentally happens frequently during a war or famine so that it's not just a slight change in food per person), that we transition into higher death rates than birth rates.
My point here is that the dynamic between population growth and decline doesn't gradually nose over as food supply and wealth dwindles.
The original response was to your notion that developed world affluence keeps population growth in check. I'm pointing out that wealth actually helps populations grow. I generalize wealth creation as the result of capitalism, and opposition to it as socialism.
And I'm pointing out that you are merely wrong here. We have lots of evidence that wealth at all levels of modern human development correlates with lower population growth. Your generalization is wrong as well. Capitalism is not defined as things good for society, such as creation of wealth, and socialism as things bad for society, such as taking wealth away. They are merely somewhat different approaches to similar problems.
Chinese and Venezueleans may call themselves socialist, but if their action is to support an activity that ultimately helps grow wealth (which in turn grows the population), they are actually supporting capitalism. Socialism is to reject that activity out of some twisted sense of obligation to some "greater good".
So call them "socialists" because of their actions then. It's a silly argument to make and again depends on a white hat/black hat view of capitalism and socialism which isn't true.
I personally heavily favor capitalism in a society, but I don't make the mistake of discounting socialism policies just because because they don't work at the huge doses that have been tried over the past couple hundred years.