What if government steps in as buyer, or massively subsidises? It wouldn't all be built in one go so it would be bit by bit. I can see it being subsidised at a minimum.
Personally, I think the houses would be filled. I just don't think it would in any way help the island's economy. It would just increase the scale of everything: more people, more costs, meaning no real advantage has been gained. The only way to gain an advantage would be to encourage people who pay more tax. I don't know where those people would come from, but short-sighted government won't think that far ahead. They will see thousands more people and think it will magically bring in money to the Treasury. And it will, but it'll also mean more money going out of Treasury.