If you have a HECS debt, you should stay tuned to what the Abbot government is doing. Currently, you are required to pay your HECS through compulsory contributions based on how much you are earning (if you are working), if your earnings are over a certain threshold. This is taken out of your salary like tax. The Australian Government does not currently have the power to do this in relation to foreign income (although the government is looking into some sort of reciprocity thing in New Zealand I think). So if you aren't earning any Australian income, then no you will not have to pay HECS. But you should be aware it is indexed annually and will therefore continue to increase in amount, regardless of whether you are paying it off or not. The ATO website has a lot more information about this and I would suggest you have a look there.
Now depending on what the Abbott government do, this could change as they are talking about charging interest on HECS debts which may or may not be imposed retrospectively on current debts. This means that while you're not earning income in Australia, you still won't be required to pay off your HECS debt, but your debt won't just be indexed, it'll incur interest and you'll want to be more actively paying it off, because you'll end up with a massive debt otherwise. For this reason, I suggest you pay a bit of attention to local politics. It surprises me how much people don't pay attention to the things that affect them...