Interesting idea. Probably not at all a legal
possibility, but interesting none-the-less. I'm a bit of an islomaniac myself and wrote about a few uninhabited islands that you could potentially
sail to in this post
. A few examples are:
Henderson Island (Pacific Ocean) - There's history
here with a visit by the whaleship Essex in the early 1800's and close Bounty neighbors on nearby Pitcairn.
Bouvet Island (Atlantic Ocean) - Not at all tropical, but you'll definitely have isolation and "wild" times.
You might also consider Jon Fisher's book called Uninhabited Ocean Islands
. It's a bit dated, but is still a fun and quick read for someone dreaming of their own island.