From the introduction on gRPC:
In gRPC a client application can directly call methods on a server application on a different machine as if it was a local object, making it easier for you to create distributed applications and services. As in many RPC systems, gRPC is based around the idea of defining a service, specifying the methods that can be called remotely with their parameters and return types. On the server side, the server implements this interface and runs a gRPC server to handle client calls. On the client side, the client has a stub that provides exactly the same methods as the server.
The above paragraph talks about a client and a server, with the former being the one who is invoking methods to the other. What am I wondering is: can the server-end of the connection invoke methods that have been registered on the client?
No, a server cannot invoke calls on the client. gRPC works with HTTP, and HTTP has not had such semantics in the past.
There has been discussion as to various ways to achieve such a feature, but I'm unaware of any work having started or general agreement on a design. gRPC does support bidirectional streaming, which may get you some of what you need. With bidirectional streaming the client can respond to messages from server, but the client still calls the server and only one type of message can be sent for that call.