Yes, but he must have a visa, all visitors to Australia apart from New Zealand citizens must have a visa. He must have applied for, and been granted, a visa. So, I see no grounds for Border Force to deny him entry as he would also have had to obtain a Travel Restriction Exemption. On what grounds can they deny him entry after granting a visa and a travel restriction exemption? Plus, I doubt whether Border Force (there's a newspeak name if ever I saw one) can release the grounds for his exemption either as there would be privacy laws they have to abide by.
Morrison is just grandstanding and deflecting as applications for a visitor visa (probably some sort of work and holiday visa) would not have much at all to do with him. If Novax is allowed in the country it will only be because the visa rules and the vaccine exemptions relating to the travel restriction exemption allow him to enter the country.
DS