Timeline bosses have two types of specific drops. Common drops and uncommon drops. They will always drop one of their two common drops and increased item rarity has no effect on that.
They will occasionally drop one or more of their uncommon drops as well, and increased item rarity does increase that chance. Twisted Heart of Uhkeiros is an uncommon drop so it is helpful to try to get higher increased item rarity when farming it.
It's also probably worth mentioning that all timeline bosses have at least one uncommon drop that is specific to empowered timelines. In the case of the Emperor of Corpses, that is the shield, Horns of Uhkeiros. Its presence as a possible drop has no effect on the drop chance of Twisted Heart of Uhkeiros, so there's no point in doing non-empowered timelines just to avoid it.