With the Squeezebox and Slimserver, it’s somehow possible. Not sure how much in sync they are, I’ve read reports from good to bad. The Soundbridge can also see a Slimserver installation, but I’m not sure if that isn’t just some very basic access and could be sync’ed like Squeezeboxes.
Another thing, since what was mentioned was “on the same computer” in addition to the Soundbridge: what about misusing transcoding to use a split copy of the stream to output directly? As long as there are no timeouts on the Soundbridge and if it is possible at all to pipe a stream to two destinations with simple methods…