Angeletor,
I could stand corrected but your posting reeks of fairly good english!! Having said that, to be able to be issued a NZ ATCO licence you must have passed the English Language Proficiency test. This is a CAA (the regulators) requirement, not Airways. I would doubt (but could be wrong) that Airways would employ someone in the 'hope' that their english would come up to speed as time went on. No harm in trying though. Good luck.
PS. even english speaking people must provide evidence to NZ CAA of language proficiency attached to the application for an ATCO Licence. (That's not a trainee licence, but the actual ATC licence)