Tuon says herself in WH that she has to make contact with the Dragon Reborn as soon as possible, because of TG and the Prophecy. And that was some months ago. Now, the Seanchan have seen e.g. ghosts and Shadowspawn, so it's certainly even more urgent.

And as said, from the quotes I cited I think one can deduce that it's not crucial to bring Rand before the actual throne ter'angreal, as some readers believe. Rand just has to swear fealty to the Empress - who basically is the Crystal Throne - and serve her to fulfill the Prophecy in the eyes of the Seanchan.