Certainly, she was a thorn in his flesh. You don't want someone like the Dragon Reborn unchecked. And she is the only one we've seen be consistently immune to his ta'veren effect. Even Tuon caved, eventually. The Pattern seems to have scrambled a lot to make sure that there was a political and military counterweight to Rand before he headed to Shayol Ghul. As it turns out, even there he needed her to come cut his emo nonsense to size. Had their positions been reversed, I suspect Rand would have been doing similar things for Egwene. Its like saidin and saidar. They work together, but they don't mix very well, and they often oppose each other too, to achieve the grand design of the Pattern.