"1. I suspect that Australia has not reached the point whereby the series is convergent?"
I suspect not.
2. does the simple geometric series model infections as opposed to deaths? My suspicion is that the model equation would be more complex.
Because - ceteris paribus - the mortality rate is likely to be a constant over time (over reasonable time frames, that is), it should make no difference whether the parameter is infections or deaths. (Although I'm not sure of the relevance of the question, to be honest).
3. You sound certain that the modeling used by the biostatisticians would not have used this in their analysis. Can you be categorical?
Well, to the extent that their predicted results look nothing at all like the growth-decay function of virtually all viruses (the modeled predictions have invariably proven to be several orders of magnitude too high), I'd guess that what they are doing is assuming in an exponential growth phase which is a lot longer than actually happens in the real world to a virus which has a Gompertz function fit applied to it.
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