This WoB was recently posted to Arcanum.  This heavily, heavily implies Odium and Autonomy have at least an understanding between them that they won't go after each other, if they aren't outright allied.  The two shardholders were lumped together by Hoid in the Way of Kings letter to Frost.   I wonder if Bavadin / Autonomy will send someone to send an Avatar to Roshar as they might be upset that someone killed Rayse if they had a pre-ascension relationship and a post-ascension alliance. Not all the Avatars do, but Bavadin might.  Autonomy can mold their Avatars in OB Ch. 50 epigraph they mention instilling a new Avatar with an intense dislike of Hoid. Bavadin might make one that's really not happy about what happened to Rayse.