No. GRRM is a capital-R Romantic, producer and writer of Beauty and the Beast, etc. He’s not going to waste an opportunity to have his white-haired pretty boy think of his doomed love with his dying breath.
Because, yes, Rhaegar was obsessed with prophecy. But Rhaegar was also obsessed with music and poetry, and well, Rhaegar. He’s not going to screw up his Byron Moment.