No; like I say, I don't believe Australia permits the export of wild-caught wildlife without strict permission. Open vs. closed bands are not really any different aside from some breeders preferring one over the other for various reasons, as far as I know it doesn't mark the bird as different in any way.
Where did you get the bird? Breeder? Pet shop? Shelter?
EDIT: You might have misinterpreted a source saying that Quarentine bands are often open-bands; sometimes adult birds are banded and need open bands as they are too big to have their feet placed through closed ones.
EDIT 2: Here's a source that explains differences in split and closed bands Parrot Rings - Types & Colours - The Parrot Society UK
It highly depends on region and practise, but there is no universal rule that an open or split band is for wild-caught, especially since CITES-listed parrots should have papers, and the VAST majority of common parakeet species such as our beloved cockatiels should come from the domestic gene pool
EDIT 3: The legal status of wild-caught 'tiels is bothering me, so I have emailed the Australian Government for an official reply