>>Is my undestanding correct, please ?
Yes, that is correct.
While your migration need to keep in mind that when child SS is moved to parent NS, the child agents will not work with that SS anymore. Means if some PackageServers are moved from child to parent, then child clients will be downloading packages only from other child PS-es or from the child NS directly if no other PS is available on the child.
One of the approaches to that kind of migration on big environments sensitive to the infrastructure configuration change is to create new Site Servers (exact copy of child ones) under parent NS, then move clients to parent NS then delete old Site Servers. In that way the clients are always using the same infrastructure and the same amount of SS-es.
Another approach is to move SS-es and agents by chunks, e.g. move quarter/half SS-es to parent, then move quarter/half agents to parent, and so on.
In the case when all SS-es are moved to parent NS, the child clients will direct all the load to the child NS, until they are moved to the parent NS also.
All those scenarios are valid and selection actually depends on your environment, configuration and free resources available.
Regards,
Roman.