Two thoughts, both wild speculation.
First, I think him leaving on his own might be a plausible plot. A lot of people in his situation would see just running away as preferible to facing disappointing their family. His story could become one of the recurring interludes. The consequences of killing sadeas, and reconciliation with his family and the law would be put off until significantly later in the main plot.
Second, shallan was able to loan pattern to kaliden durring the Chasmfiend fight scene. And we have many insences where bonded spren interact with people they aren't bonded to. If adolin is able to at least partially recessatate his blade, but unable to transfer the bond, you'd have a very interesting set up. We see several relationships between KR and their bonded spren, but a relationship between adolin and a broken spren that's still bonded to a dead dude who betrayed her would be a cool indeed. This would also elevate adolin to were he would once again be relivent in combat, not on par with a full radiant, but something in between.
Wild Wild speculation
Related Side note; do we know if once a radiant dies, their spren are forced to return to shads-mar or can they stay in the physical? And if they can how long until they lose their consiencness? Or do they?
Thanks