Your arithmetic is wrong. You've confused (tera)watt-hours (a unit of energy) with (tera)watts (a unit of power - that is, energy per unit time). You've also "upgraded" the Snowy almost 300-fold (3.7 GW -> 1000 GW).
Doing it properly:
Australia uses about 200 terawatt-hours (TWh) per year.
200 TWh/year * 1/365 years/day * 1/24 days/h = 22.8 GW (a little under a third of Australia's peak generating capacity which in 2014 was 66.6 GW).
So, we're talking closer to the ballpark of 10-20 Snowy schemes, not 200.
