No. I've known a number of Americans who have been in Australia for 20, 30, even 50 years, and still sound as American as ever. Perhaps Americans might listen to them and think they're beginning to sound Australian, by to my half-Australian-half-English ears, they still sound quite American. The same goes for Scottish people - Scots never lose their accent. On the other hand, English, Irish, Welsh, and Canadians all tend to lose the accent after enough time in Australia (depending, of course, on how much the socialise with other English/Irish/Canadians). I'm not sure why American and Scottish accents stick around so much, even if you come out as a teenager. (Younger children, of course, can lose the accent, but there's a girl in my sister's class at school, 15 now, has been in Australia since she was about 8 and lived in America before that, who still sounds quite American. Then again, she openly claims to hate Australia and can't wait to move back as soon as she's old enough to go by herself, so maybe that has something to do with it).
Also, I strongly recommend that you don't try to "put on" an Australian accent! Even if you've lived here for years, your accent has faded slightly, and you feel you've got the accent pretty much perfect when you practice to yourself and your American friends, Australians will pick up on you and get offended! I don't know why, but that's how it is - Australians get offended when people fake the accent, and NO-ONE (except possibly Kiwis) can ever fake an Australian accent and get it right. They might get close sometimes, but an Australian can always tell, and with their tendency to still pronounce Rs, Americans usually come out sounding more Irish than Australian.