In my opinion, no. Practically speaking it's binding, and the judge's decision is legally binding, but the arbitration itself is not _legally_ binding in that subsequent judges in many jurisdictions can choose to ignore the arbiter with zero repercussions in law or precedent.
Your second phrase does not follow from the first one, at least I can't follow it.
If the judge doesn't override the arbiter most of the times, doesn't that implicitly make arbitration... legally binding?