No, the branch is an illegal person and is not eligible to apply for a patent. It requires a unit or institution with legal personality to apply.
Legal basis:
Article 37 of the Patent Law of the People's Republic of China If the application is stipulated by law, the applicant shall be notified and required to state his opinions within a specified time limit or make modifications to his application; if he fails to respond within the time limit without justifiable reasons, the application shall be deemed to have been withdrawn.