I agree for the most part, though ultimately I'd think someone would be living in the larger islands by the modern day. There are plenty of islands that were uninhabited when European explorers first visited them that now have thriving human societies - Madiera, the Azores, Cape Verde, Bermuda, South Georgia, St. Helena, the Falklands, Pitcairn, and Norfolk, to name the more significant ones. The temperate and mountainous parts of New Zealand would probably still be settled by Europeans, while the islands with tropical climates might see settlement by indentured labor from India, the Philippines, or Indonesia, perhaps. I could see the Spanish attempting way-stations between the Philippines and New Spain that develop a hybrid culture of Filipino and Central American influences, while the British might send Indians in the same way that they did to Fiji and Guyana.