They could probably get some appeals court to agree with them, maybe. The catch is defending it. Not against established countries, but against other non-state actors.
Meaning, brigands, somali pirates, al qaeda types. They aren't there to take your sovereignty, of course, they're there to rob you or kill you, and you're safely beyond the jurisdiction of any country's coast guard. Dial 911 and no one's coming.
A few years ago I wouldn't have given this a second thought. In the current world as it is, a ship, a floating platform, whatever, will have to provide for its own defense at least against any reasonably likely threat. I would suggest a robust "right to bear arms" for anyone planning to live out there. Or hire gurkhas. Or both.
If they offered illegal genetic engineering / fixing, they would definitely risk eco-terrorism.