Wouldn't Rand faking his death cause more chaos making the Dark One more powerful? The Dark One seems to feed off of disorder.

In KoD, there was a scene where the common people were asking "where has the Dragon Reborn gone?" and that was raising a concern. It seems to me if people KNEW that he was dead, most people would lose hope and the Dark One would win just from the fact that people believe he is dead. They have a lot of faith in the KC prophecies, or rather the Nobles do (those who have read it). The common folk will follow their lords. Seems to me that the only thing holding most lords back from revolting and trying to claim power is because of Rand. If you take Rand away, it'll probably be a Civil War scene while you have misc people trying to claim throne and power. It won't matter that Logain is in charge, Logain is not Rand.