Can the ESXi host on which vCenter resides be upgraded without migrating the vCSA?

The statement that the vCenter Server Appliance (vCSA) must be migrated away from its current ESXi host before that host can be upgraded is correct because vCenter manages the ESXi hosts and their associated virtual machines, including the vCSA itself. Performing an upgrade on the host that is running the vCSA could disrupt the functionality of vCenter and lead to potential stability issues during the upgrade process.

Moreover, vCenter is tightly integrated with the underlying ESXi host, meaning that upgrading it while vCSA is still running could result in compatibility problems. For these reasons, it is crucial that the vCSA is migrated to another host prior to the upgrade to ensure that the vCenter services remain uninterrupted and maintain compatibility with the new ESXi version.

While there may be considerations for specific scenarios or advanced migrations in different environments, as a general rule and best practice, it is recommended to avoid upgrading the ESXi host that is currently running vCenter without proper migration first.