U.S. would not have been able to contribute as member of the tribunal even if it was a party to UNCLOS
First, while the United States has a strong interest in peaceful resolution of competing territorial claims in the South China Sea, it is not itself a claimant, and thus UNCLOS would provide no additional tools for the United States to use in addressing disputes in the South China Sea. While U.S. ratification of UNCLOS would allow U.S. nationals to serve on arbitration panels, such representatives are expected to exercise independent reasoning and do not take instructions from member governments.
If anything, the presence of an American on the panel would have played to the suspicions of hardliners in China who view international legal regimes as a vehicle for advancing U.S. interests. If this sounds farfetched, consider that the Chinese ambassador to ASEAN recently accused Washington of “staying behind the arbitration case as the manipulator, and doing whatever it can to ensure that the Philippines wins the case.”