Not sure what you mean by broadcast streaming. What I do is run the daemon on the server and feed it with music using either an mp3 player on the server itself or winamp running on a desktop. Then it is playing the whole playlist constantly until it ends or I stop it or I can have it on repeat to never stop. Then I just use any mp3 player on any machine on the network and listen to the broadcasted stream playing from it.
The music does not start over or change songs when connecting to it from different clients, it just keeps playing weather your listening or not.
Shoutcast also allows you to play individual songs on the fly but I haven't played with that feature much to know enough about it.