Yes. Foreign companies can apply to become auDA accredited registrars.
The registrar must meet the following criteria:
They have to be registered to trade in Australia, which means that they must register an Australian Registered Body Number (ARBN) Australian Securities and Investments Commission (ASIC).
More information on registering an ARBN is available on the website at http://www.asic.gov.au/asic/asic.nsf/byheadline/Foreign+Companies?opendocument.
They must register with the Australian Taxation Office (ATO) for a
Australian Business Number (ABN) and Goods and Services Tax (GST).
More information about ABN and GST registration is available on the ATO website at http://www.ato.gov.au/Business/GST.