No, it wouldn't come close to doing that. It would flatten and burn cities, military bases, and missile silos that were targeted, and irradiate places downwind. But there's much more land that would not be targeted and isn't near those sites.
For example, what would be the reason to nuke the Amazon, the Arctic, or the Himalayas? How much of Africa would be targeted? What percentage of the US Midwest or Siberia do you suppose would actually be irradiated? What about islands in the Pacific? Is Easter Island going to dosed in lethal radiation from fallout tens of thousands of miles away?
for MAD to work all you need to assure is that you can damage the opponent enough that their power structure will not survive, not to destroy all of their people/land/capital.
For example, what would be the reason to nuke the Amazon, the Arctic, or the Himalayas? How much of Africa would be targeted? What percentage of the US Midwest or Siberia do you suppose would actually be irradiated? What about islands in the Pacific? Is Easter Island going to dosed in lethal radiation from fallout tens of thousands of miles away?