Yes, a blocking operation in a Service will still block the application. Despite first appearances, Services are not simply for running tasks in the background. They are for running tasks with a lifecycle that is independent of the Activity lifecycle (IE, they may continue after the Activity is closed).
A Service that starts and ends when an Activity starts and ends when the Activity ends is useless.
In your case, where you are streaming audio, you may want to stream audio even after the user closes the Activity, in which case, you should use a Service, but you’ll still need a thread (or an AsyncTask) for blocking tasks.