If the Narutoverse is politically similar to our world there won't.
If the Shinobi Alliance win the war, there'll be no civil war since a new world order would emerge, where globalization takes place. This means that there'll be probaly a United Nations for Narutoverse, a global army like the UN peacekeepers, international laws, and so on. Countries will lose much of their sovereingty and merge together as one big country. Civil war is also not possible because after the war all organizations, parties and clans would have been weakened due to war, and only the shinobi nations would have true power, since their counter part has been eliminated. This would cause the feudal lords to have monopoly on power.
It's just like history. Think about the cold war. When the west was "threadened" by communism, they solved their problems and united to fight the emerging communism east. They created NATO, a military alliance, just like the shinobi alliance. Now that USSR ended and they have no more reasons to keep NATO, NATO is still up and very well. It has been even deployed in most recent wars like Kosovo and Afghanistan. This means the west as we know (US and western Europe) is still together because they noticed that together they have monopoly of power. That's what shinobi alliance will do when the war ends (if they win).