Probably..... not.Who did they trade with then? The invisible man and his invisible government on behalf of the invisible citizens living there?
Likely the trade was conducted on the mainland by a company that somehow obtained letter head or a license under the authority of the Heard and Macdonald islands.
A few decades ago, there was a rush of Made in the USA labels regarding clothing made on Saipan (USA, but not USA in the full sense regarding safety enforcement and working conditions).
I would not be surprised if somebody, somehow saw a monetary advantage to obtaining say a "Heard Island" label / origin and then figured out a way to get one- even if nobody actually lives on the island. Must have been a neat trick.