I absolutely would try my best with that treadle. The chair would need to be re-caned, but there are people who can do that, or show you how to do it. The treadle base needs care and attention, but it can be done, even if the veneer is perished the wood will turn out beautifully - hopefully there is no woodworm in it? If there is woodworm, it will take a bit longer, providing the base has not been feeding a generation of worm. The machine will take longer to fix than the treadle and the irons.