I think you are missing a few key external inputs with your theory. Yes populations in Western and Asian societies are predicted to drop, however African populations are still predicted to rise and that will blunt the level of population decline overall.

We may not be able to adapt our agriculture and industry to climate change fast enough. Once these industries suffer catastrophic setbacks or supply chain disruption they may never come back on line especially if we live in a world of constant crisis and change.

Finally there are external inputs that humanity doesn’t control that may take the place of industrial emissions which could create a feedback loop that humanity can’t break even if we set our emissions to zero. Google methane release from permafrost melting of you want a good example. There are also large stores of methane deep within the ocean that could be released if sea temperature rise as well.

There is a very good chance that if humanity enters a climate change induced “dark age” that we may never recover as a species. Most of the easily accessed resources that underpin our society were exhausted early on in our industrialization. A society trying to rebuild in the aftermath of a complete collapse may not be able to rebuild as there are no easy resource inputs to harvest to jump start the process. We may not get a second chance to correct our mistakes as a species.