Yes you will need to have the vessel registered before we Aussies let it sail out. And I would assume every nation on your way home would also want it registered to one country or another. The best option for you will be to try and have it registed in the USA straight away. Being a US national it will make your paperwork easier as you go from port to port.
I am an Aussie looking to buy in Greece
in a year. And have been researcing the alternatives. In my situation, the vessel doesnt have to be in OZ to be registered. It can be done long distance as long as the small forest of paperwork is filled and filed accordingly.
I was warned about being one nationality and owning a vessel registered elsewhere. Some more paranoid officials at varying ports
may think the boat is stolen or drug running etc.
From an Aussie law perspective, I wont have to pay GST until the boat arrives here. Perhaps US law is the same.