Ms Hunt said the party was culturally significant.
She asked for interim name suppression on the grounds they would suffer extreme hardship, including the identification of their company.
"They risk the loss of the company," she said.
Immigration NZ lawyer Saar Cohen-Ronen asked for suppression to be declined, saying they had known they were under investigation for some time.
Judge Behrens granted them interim name suppression until next month.
He remanded them on bail and excused them from attending their next hearing.
They must advise Immigration NZ of their intention to travel and their itinerary before leaving the country.
Three others arrested in the same investigation were also granted interim name suppression and bailed until their hearings next month.
Immigration NZ has investigated 33 employers between last October and September this year, including 10 which are still under investigation.