Do some research Ogs, perhaps looking
HERE which gives the synchronisation coverage area?
It appears they rely upon synchronising with the time based WWV RF signal on 5 or 15 Mhz from Colorado, amongst other stations in North America. The signal is hard enough to receive in Australia with a decent antenna and receiver (due to a high signal to noise ratio on HF frequencies), particularly during the day, so my guess it is most unlikely the watch will synchronise in Australia.
But I may be wrong......