Maybe?
Rhaegar annuling his marriage to Elia would certainly forfeit the support of House Martell, which would be a bit of a problem since the Martells were the only Great House in Rhaegar’s camp.
But then again, Aerys had a strong tendency to view everything as a Dornish plot against him – hell, “when the news” of the Battle of the Trident “reached the Red Keep, it was said that Aerys cursed the Dornish, certain that Lewyn had betrayed Rhaegar,” despite the fact that Lewyn Martell died fighting at the Battle of the Trident.