According to Hofstede's cultural dimensions theory, the USA and Australia have very similar cultures, although 'mateship' is not a dimension considered I will admit. :D
I would suggest that all national cultures value loyal friendship and working as a team.
That said, 'mateship' has a sense of egalitarianism to it, and while Australia and the USA are egalitarian cultures, that is lacking in other nations, e.g., China.
Australia and the USA have deceptively similar cultures. On the surface we are very similiar, but there are a lot of important differences that can bite you on the backside when you least expect it. Group dynamics are probably one of the more important differences.