Does `timeout client` play a role while proxy is waiting for response from server to send back to the client?

This is one thing I can’t get clear answer on. If some time period Y elapses since the connection to the server was established, without the proxy having received any response data from the server to relay back to the client, does this time period Y count against the value of timeout client? Consider a client that successfully connects to the proxy and manages to send it enough of a request the proxy is ready to start forwarding it to the server, but where the server then takes a long time to process the request (slow storage link for storing request data etc) before it can even generate the response status line – does all the idle client connection time count against timeout client? I hope I am being clear with my explanation and not being self-contradicting.