1. She's a a sitter, but little above that is known of her.
2. Quite importantly, she is / was not on Verin's list of BA. Technically, Mesaana is not a BA, so this would not even be a mistake by Verin. IMHO it is quite unlikely that Verin should miss a BA in such a position.
3. I think that Mesaana somehow learned of Egwene's coup with the rebel BA and chose to leave the Tower, possibly to arrange a rallying point for all BA some days later. Maybe it even was Alviarin who warned her. Though the OR would likely not expose her, I believe that she's too arrogant to allow a binder used on her, no matter which ways she might have to remove the oaths.
4. I wouldn't discard the possibility that Mesaana already left the Tower at the beginning of the Seanchan attack, evanding the risk of getting collared. I will look it up later, but was Evanellein still there at the end of the attack?