As other respondents have said, (a) it depends, and (b) they do. Reflecting on the Asian Australians I’ve known in the past thirty years:
- People who’ve come off the boat naturally aren’t going to have an Aussie accent. Duh. Although I’ve spoken of a counterexample here: Nick Nicholas’ answer to Who are some people you know who became fluent in a foreign language as an adult?
- Second generation Asian Australians will, by default, have an Aussie accent. Of course. I haven’t noticed someone who doesn’t.
- In fact, I contrast second generation Asian Australians with second generation Greek Australians. There is a distinctive Greek-Australian accent that I can pick out in 40 year old and 50 year old 2nd gen Greeks: it’s not Greek at all, it’s overcentralised, and a little overenunciated. I don’t recall something similar with Asian Australians. But as I keep protesting, I do have a tin ear.
- Some Asian Australian schoolfriends and acquaintances have been on the Cultivated Australian/Vaguely British side. That correlates with Taiwan (not sure how), and with Hong Kong (a bit more obvious how).
- On the other hand, my fellow engineering student from Shepparton in rural Victoria, predictably, had one of the more ocker accents I’ve ever heard. Mate.