Legal analysis: No, if the trustee does not sign the power of attorney, it means that the trustee has not accepted the entrustment of the parties, so the power of attorney has no legal effect.

Legal basis: Civil Code of People's Republic of China (PRC).

Article 165 If the power of attorney is in written form, it shall specify the name of the agent, the matters to be represented, the authority and the time limit, and shall be signed or sealed by the principal.

Article 919 An entrustment contract is a contract in which the principal and the agent agree that the agent shall handle the principal's affairs.