Yeah, I can pick out Melbourne vs Sydney accents, and even Sydney East vs North vs West (and the various cultural group differences such as Mediterranean-influenced Australian), but it's not something most people would pick up on, even many Australians. Someone from out in the country is gonna think the West and upper North has harsher vowels than them (a holdback of First Nations English vernacular) and the others are just posh city boys.

It's more like someone from London being able to pick up what street you're from.