I think the answer is the opposite. Consumption of resources is proportional to standard of living: it takes resources to make the most modern lifestyle available. The demographic collapse, however, is evident in highly industrialized societies like Korea, while backwards regions with a low standard of living still have high birthrates. Subsaharan Africa, for example, consumes less than Korea per capita but has a higher birthrate. It seems more likely that higher rates of resource consumption are correlated with lower birthrates.