A 56 should not have the pipe - I think you need to have a look where it goes in your car - I "believe" the pipe was originally fitted to a pump situated near the front bumper (sorry, I don't have a diagram and my memory is a bit shaky as it was so long ago) - the pump was there to push air into the system when the car was cold to help keep the exhaust gasses clean - its thought that the SAI system was included to conform to Euro emission rules that never came in, hence it was removed from cars after 2004 (cost cutting).
You could also have a look for the check-valve which is a silver disk top of the engine, middle right. If I am right, your car wont have this (perhaps others could confirm). Its worth knowing because the check valve can go wrong resulting in an expensive repair and its not too difficult to maintain/replace.
People used to do all sorts of daft things to their air boxes to try to improve performance, but the saab air box and filter was actually pretty good. You can see that the screws on yours are wrong - they should be black/hex, not shiny. It might be that your looking at a bad replacement and the hose goes nowhere - it will be interesting to find out.