Yes you do, but the GST saving is only actually on the difference between purchase price and residual value in the long run (when the lease ends if you take ownership you pay GST on that amount). It therefore depends how long you lease for, your taxable income etc. etc. Lots of different scenarios that could exist.If you initially purchase the car through finance, then resell to a leasing company, wouldn't you lose the GST benefit?
The ATO's minimum residual value after 3 years is around 47%, so if you leased for that length of time you (sort of) only save 53% of the GST.
Agree it is better to lease from the start, but I don't like the risk that if something did change in the bill I could be stuck with a much more expensive lease with no major tax benefit. To me this way is a bit like buying insurance, I pay a bit more to mitigate a greater risk.