Legal analysis: No, if the contract witness doesn't sign the contract when it is established, then he can't sign it afterwards, because it takes time to witness it. In fact, in the contract witness, only the witness's signature is valid. If the witness does not sign, the contract signed by the parties is valid.

Legal basis: Article 502 of the Civil Code of People's Republic of China (PRC), a contract established according to law shall come into effect upon its establishment, unless otherwise stipulated by law or agreed by the parties. In accordance with the provisions of laws and administrative regulations, if the contract should go through the approval procedures, such provisions shall prevail. If the failure to go through the formalities such as approval affects the effectiveness of the contract, it will not affect the performance of the obligation clauses such as approval and the effectiveness of relevant clauses in the contract. If the party that should go through the formalities for approval fails to perform its obligations, the other party may require it to bear the responsibility for violating its obligations. The modification, assignment and dissolution of a contract shall be subject to the provisions of laws and administrative regulations, and the provisions of the preceding paragraph shall apply and shall be subject to approval.