6 billion people depending on overconsumption of fossil fuels was already considered an unsustainable death spiral for human civilization, back in 1996.
But no, civilization would probably not collapse, if we culled 2.6 billion people... as long as the 6 billion survivors get to keep overconsuming fossil fuels at *at least* 1996 levels. The situation looks even better if we make sure to cull 2.6 billion old, infirm, unemployed, or otherwise net consumers of everyone else's labor output. Civilization is less likely to collapse if your population control focuses on people who are no longer contributing, or not currently contributing, or not capable of ever contributing.
But I doubt that's what you have in mind.