Yes, I think the story made it if not for Fatima's anger Sorghaghtani would just give up, but because of what Fatima did she will keep fighting for the Throne and follow real story.
I like the characterization of Ogedei as kind of a drunk goofball and Boraqchin as the insanely loyal first wife scheming 24/7 to cripple the competition while he's totally oblivious.
Making Fatima the one who convinces Sorghaghtani to fight is delicious irony.
If Tolui's holdings got fully absorbed by the Ogedei side, Tolui's sons would never become khans and the horde would've probably collapsed a century earlier, sparing the Arab world and China/Japan/Southeast Asia from the Mongols.