It is possible to complete the acquisition without obtaining approval from China. There have been numerous instances where this has been the case, with the Dell/EMC merger serving as an example.
Mergers and acquisitions that have faced obstacles due to a lack of approval from China typically involve companies operating within the same industry, where the combination of operations offers substantial economies of scale. For instance, the Intel and Tower merger encountered difficulties as they couldn't operate independently in China because part of their business case relied on merging production facilities. On the other hand, BC and VMW operate in complementary sectors, representing a new line of business for BC. Redundancies in roles for BC/VMW are primarily outside of China, such as in the US, UK, India, and other locations, where production and operations are separate. For instance, VMW does not manufacture or develop products in China; they focus on sales exclusively.
Note for VMware employees: The internal unofficial Slack channel has more relevant information than this medium and people there are not anonymous. Therefore, offering accurate and honest information. Here, there are even non-VMware people who are just "fishing" for insider information.