Doubtful.
An enemy will capitulate too quickly. It's not like countries could be shooting nukes at each other for 4 years. One or the other will take a devastating hit to the political center, and sue for peace before the world gets destroyed. It could conceivably be after ONE shot - a couple million killed at once - that sort of thing.
You wanna kill 7 billion peeps, you need "bugs or drugs." 'Cuz ideally, the elites who pull it off, don't want to spend the rest of their 150 year life span in a bolt hole in Borneo. They want to be out in the beautiful world.