That theory assumes that growth can be virtually unlimited, when it's not. At this point in time, the only energy source we have that can deal with providing the transportation, food growing, and energy needs of the population is fossil fuels. If we continue using fossil fuels at an ever increasing rate, global warming is going to decimate food production. And millions upon billions are going to starve to death, if we aren't killed off by some plague or a nuclear war first.
Still, it does bother me that the biggest population growth centers are those least capable of supporting an increasing population. That makes the likelihood of wars that much greater.