To directly answer the specific question ask I think that that sort of thing IS a singularity in the sense that it's a point in time that current rules and understandings do not let us see through. There is simply no amount of theorizing that will let you look from now through that sort of event to what is on the other side. There are climatological impacts beyond the article referenced, political effects, etc. Too much depends on the response from inside the developed nations. Do they focus on technological solutions to the problems? Do they waste precious time blamestorming and second guessing? Do they turn their back on that part of the world and "let nature take it's course"?
Too hard to guess, the current practices and attitudes break down in the gravity of that sort of event.
Last month I was involved in a conversation thread about what the impact of a hypothetical nuclear war would be on existential risk.
There are many potential nuclear war scenarios which would have varying impacts on existential risk. It's difficult to know where to start to gain an understanding of the long-term of nuclear proliferation.
For concreteness, consider the case of an India-Pakistan nuclear war.
According to Local Nuclear War, Global Suffering by Robock and Toon,
[...]
Note that this would presumably cause some degree of chaos in the developed world.
I have not yet investigated the credibility of the papers' claims. However,
Suppose that an all-out nuclear war between India and Pakistan were to occur and were to result in climate change killing 1 billion people. Then would the probability of a positive singularity increase or decrease and if so why?
This question seems very difficult to answer; maybe altogether too difficult for humans to answer. I welcome responses raising relevant considerations even in absence of a good way to compare the relevant considerations. Please read the linked conversation thread before commentating.