Possibly, but if your talking about an actual nuclear exchange rather than a rather dramatic reenactment of the French Revolutio it would probably just make things much much worse for the climate. Your at most looking at twenty five percent reduction in humans, and the remaining seventy five percent will probably be too busy repairing and rebuilding infrastructure to prioritize further emissions reductions.

Indeed since you now have a demonstrable reason to dedensify urban areas in favor of small towns, becuse things like batteries and solar panels have complex global supply chains while for much of the world oil, gas, and coal are available close by with easier to build infrastructure, and because you now need to make a vast quanty of new stuff to replace what was lost, well net result would almost certainly be a small drop followed by a continued increase in emissions for the next few decades before things got back to normal and decarbonization efforts could resume, now aiming to limit things to 4 to 6C.