Kind of like I mentioned in an earlier post, this would be very destabilizing for Dany, not just in terms of her claim, but her sense of purpose. Her entire life is going to be turned upside down. This might be where this season ends, actually, with her on the verge perhaps of finally taking the throne, or having taken it, to have it taken out from under her.
I go back to her vision at the end of season 2, in the House of the Undying. She enters the throne room which has been partially destroyed. It is winter. She approaches the throne, intent to take it, but then leaves it behind. She follows the cry of the dragons out the gate and through the Wall. I think her ultimate destiny is in the North, against the White Walkers.