The Seanchan are not a parallel to the dual wounds.

The wound is to Rand what the evil of Shadar Logoth and the Shadow are in the world: two evils fighting one another and both of them also fighting against the Light and destroying it - but if you can have them fight each other, you can make them destroy each other (in the world, the result was the Cleansing of saidin... Rand himself made the analogy to his wounds... it can't be clearer than that). The first wound Rand got from fighting Ishamael whom he thought to be the DO. The second wound came from Fain, with the dagger from Shadar Logoth.

That's totally unrelated to the Seanchan. Your analogy doesn't work at all. There's no SL/Shadow duality, and the healing of Rand's wound, whether Rand is healed or he dies from the wounds, will do absolutely nothing to solve his problems with the Seanchan. It's tied to Fain and the Shadow, not the Seanchan.