No. Only Australian-registered private health insurers can offer OSHC. Furthermore, not all Australian insurers can offer OSHC, they must first have signed the OSHC Deed with the Australian Government. This is because the Australian Government wants to be able to monitor and regulate insurers covering people living temporarily in Australia.
The Government is not able to protect the interests of people insured by overseas insurance companies in the same way. Here at OSHC Australia we compare all insurers able to offer OSHC to international students.