The action that you take actually depends on whether the Agent was enabled/running at the time when the specific desktop client application was started. If the Agent was enabled/running, the client application established a connection to the Agent and tries to reestablish the connection when it is lost. That is, every time you start, enable or disable the Agent, client applications always try to reconnect to the Agent once it's running. If the Agent was not enabled/running when the client application started, the client application does not use the Configuration Agent and does not even attempt to connect when the Agent starts. All this effectively means that:
Desktop client applications that started while the Agent was enabled/running do not need to be restarted.
Desktop client applications that started while the Agent was not enabled/running must be restarted.