Not necessarily. Although Nanjing University has to pass CET-4 and CET-6, it doesn't have to pass CET-4 and CET-6. You can apply after passing Band 4.

Nanjing University

Requirements for postgraduate degree application of Nanjing University:

Application conditions

As can be seen from the application conditions, Nanjing University does not need to pass CET-6 to apply for an ordinary master's degree, but it requires CET-4 to apply for a direct scholarship. Moreover, compared with CET-4 and CET-6, the achievement of CET-4 and CET-6 is only an additional condition. Baoyan cares more about your GPA, scientific research projects and competition experience, so the most important thing is to improve your level and get good grades. Usually, you should take part in more competitions and improve your English while participating in the project, because the latest research of the project is basically abroad. It is necessary for us to know foreign literature, and English will also be exercised. On this basis, we took the CET-4 by the way.

However, passing CET-4 is only a school's application for registration qualification, and the specific college regulations will be different. For example, Finance College requires that CET-6 should reach 500 points or above, so if possible, try to pass CET-6, lest your college is not qualified for postgraduate entrance examination, and you will suffer if you fail to meet the requirements of postgraduate entrance examination.

I hope my answer can help you, and I wish you success in your research.