Can the export of the caribbean cultural identity to the diaspora, be beneficial to caribbean islands?

Well this depends, if you are targeting a group of displaced people, that may be beneficial to the society already at the Caribbean Islands, then yes, of course it can. You may want to think of these people as potential tourists for the Caribbean Islands, and they may even want to move there. When you export a cultural identity naturally some people will identify themselves, and find themselves in that culture!