If a VPN server is connected to a VPN server through the VPN Client feature of the VPN router, can the subordinates communicate with each other?

It is possible to configure location A as HUB and interconnect location B-C.
This is a configuration (topology) commonly referred to as "hub and spoke."
Conversely, connecting all locations (A-B, A-C, C-B) is called a "full mesh."

Whether to allow inter-site communication, not limited to VPNs, depends on your organization's policy and configuration.Accept it or not, both of which are common.

For VPN connections between routers, we do not often say "server" or "client."