As far as I can work out, yes I think that's all its for. The silencer is not fitted very well so that rubber mounting is under constant stress. It was split when I got the car so I've already replaced it, but I think adjusting the silencer mounting would be better.
If it's any help, here's a sketch of my exhaust support from many moons ago. Not shown is the exhaust clamp which was welded to the top of the 'triangle'.
Note that the exhaust should be mounted solidly to the engine/transaxle so as not to flex independently.