The only airport where I have got "Priority" baggage service is LHR (and that was Terminal 4, I'm hoping Terminal 1 operates in a similar fashion).
For those who haven't flown into LHR, the priority bags always seem to come off first, and are then removed from the conveyor and placed next to a sign indicating "priority baggage". In most cases my bag has been there before me.
I think it would be useful if other could comment on specific stations where priority baggage works - as this can effect one's decision as to whether to check.