Initially, it would appear that the answer is an obvious yes. But, is it?

The Federation of Danish Co-operatives has published a discussion paper on international co-operatives:

Transnational Co-operatives: Perspectives for admission of members abroad and cross-border mergers, 2005
http://www.danskeandelsselskaber.dk

The discussion paper suggests a transnational co-operative is one which has members in two or more countries, members are equal in rights and obligations and the members have common commercial goals.

An overseas  co-operative that operates in Australia without Australian members is not a transnational co-operative. It is a national co-operative (e.g. Netherlands and New Zealand) operating as an investor-owned company in Australia - with no Australian membership and control.

The WA Capricorn Society Ltd is an inspiring example of an Australian co-operative with Australian, New Zealand and South African members:

http://www.australia.coop/publish/article_35.php