Correct. It is actually impossible for the government to furnish people with the balances promised to them by their banks, in the event of a run. Bank credit to customers (redeemable on demand) exists in multiple to the actual circulating plastic notes. The government would have to issue bonds like there is no tomorrow, and the RBA would then purchase these.
To be honest I doubt even the RBA could manage this feat. Our notes are not simple paper and black ink. We have special plastic notes - I wonder how fast these can actually be produced. The bizarre reality is that in the event of an Australian run, the most important economic influence would be the number of note-producing devices the RBA has.
Of course, one would be happy to get ones notes. One would then immediately walk to a bullion dealer.