I suspect that even if modern war dropped populations enough to dent CO2 production, the war itself would burn enough oil to offset it.
And remember, the US military is not running at full speed. It’s currently involved in a few counter insurance missions, which while not cheap are a far cry from the resources required for 2 modern nations having it out. There are fewer than 20,000 soldiers in hot spots as of 2017, out of the 1.3 million active duty personnel available. You can bet if the US were to go against China or Russia our oil usage would go through the roof.
I couldn’t find hard numbers, but the range appears to be about a billion barrels of oil per year for the US, maybe higher.
Interestingly, we used a lot less fuel per soldier then. The normal back then was 1 gallon per soldier per day. By desert storm we were up to 4, and by 2007 we consumed 16 gallons per soldier per day[0].
Now obviously we have a smaller army now, which goes a long way to explain the lower total consumption than in WW2, but it is mildly terrifying to consider what a WW2 sized engagement would consume at 16x the per-soldier fuel consumption.
0: https://www.forbes.com/2008/06/05/mileage-military-vehicles-...
A nuclear war will:
1. Kill hundreds of millions of wealthy people.
2. Is the most likely kind of 'real' conflict between wealthy people.
(I would say it's very unlikely.)
1. The US and Russia are currently doing their best to antagonize eachother.
2. The US is currently doing its best to extract itself from the tyrrany of MAD (By building ICBM defenses.) [1] If MAD breaks down, the whole house of cards that justifies the existence of nuclear weapons as a guarantor of peace collapses.
3. The Russians have an automated retaliatory-strike system - should they be attacked, it will end the world. Hopefully, there aren't any bugs with it. (But knowing how software projects go, of course there are bugs with it.) [2]
4. The decision to launch, once made by either country's leadership, cannot be second-guessed by saner subordinates.
[1] https://en.wikipedia.org/wiki/United_States_missile_defense_...
If it were that high, we'd likely have had one by now. I think it's an order of magnitude lower than that.
But much more importantly, we've all been discounting the cooling effects of nuclear winter.
I "strongly feel" it's not very likely, whatever very and likely mean, so there.