Legal Question in Construction Law in California

No. You cannot take the CSLB to small claims court. You may or may not be able to challenge a decision of the Arbitration Program, but it would not be in small claims court. It would either have to be an administrative appeal, or a lawsuit in Superior Court.

You can't take either the other party or the arbitrator(s) to Small Claims. Hearing arbitration appeals is not within the jurisdiction of a Small Claims Court. Perhaps the Superior Court would hear an appeal, but only if there were a procedural flaw in the arbitration, not because the decision, per se, was unfavorable following a proper arbitration proceeding.