I have my regular SliMP3 connected to my hi-fi amp which has speakers
in two rooms. If I added a Squeezebox [placed in the room without the
hi-fi] with no connection to the amplifier, but running in sync with
the original set-up, would this be usable with the remote control to
control the music being streamed from the SlimServer? (I am guessing
'yes', because I don't see any way that the Squeezebox would know
whether it had an amp on the output or not.)

Any suggestions about other ways to achieve the same effect would be
most welcome.