If the service is accessed synchronously, then the thread is blocked while waiting for the response. While the thread is blocked, the processor is freed up for other processes/threads of execution. If it's asynchronous, the thread is not blocked, but unless the program has busy work while waiting for the response, the thread will be idle, and will not consume cpu resources. If you don't know which you are using, then you are likely using a synchronous call.
So the answer is no, waiting for the web service response does not use clock cycles. Doubling the frequency of the calls will still leave lots and lots of idle time for the other process to function.