The EJB container implements the EJBHome and EJBObject classes.

The EJB container maintains an instance pool. The container uses these instances for the EJB Home reference irrespective of the client request. while refering the EJB Object classes the container creates a separate instance for each client request.
The instance pool maintainence is up to the implementation of the container.
If the container provides one, it is available otherwise it is not mandatory for the provider to implement it. Having said that, yes most of the container providers implement the pooling functionality to increase the performance of the application server.
The way it is implemented is again up to the implementer.