Technically I think this is not possible. From what I understand the WAAS transmissions made in Japan are referenced to GPS receivers (measuring the differential) on the ground in Japan providing the WAAS capability over that local geographic area.
I would think that potentially using that WAAS differential signal in Australia (which is essentially a time shift of the GPS signal in the receiver) could put an aircraft way off course compared to turning the WAAS signal off. GPS receivers work their positions out by looking at the time differance between GPS signals, WAAS makes an adjustment to these time series.
A receiver in Australia would see a different satellite constellation than a receiver in Japan would at any given time (a satellite that is visible in Japan could be beyond the horizon in Australia), and is the WAAS transmission is making corrections to only part of the constellation that a receiver in Australia would have visible.