Does the Chinese Visa Application Service Center belong to the Chinese Embassy/Consulate General?

No, it doesn’t. The CVASC is a commercial service organization registered in accordance with local laws and regulations and recognized by a Chinese Embassy or Consulate-General to handle the daily routine work of processing ordinary visa applications.  However, it operates independently of diplomatic missions and is neither a branch nor an affiliated organ. Please note that the CVASC does not participate in the assessment and approval of Chinese visas.