the entire war, no.
most of it, yes. We may even see the Naruto vs Tobi fight, but not much after that.
The way CC2 makes the Naruto games is they take the manga as the base for the story and structure and the anime as the base for how the characters look and feel when in movement. Storm 2 covered the pain arc only because the manga had covered it (source material) and the anime had been in the process of covering it (influential material). The only way I see the game covering the war up to what we have seen is if there are 0 fillers from now until the game's release.