Interesting query. There's two ways of looking at this, short and long term. In the short term, the answer is almost undeniably, no. Its really a variation of the "wolf boy" or "Tarzan" scenario. Would a human baby raised by some wild animal naturally grow into its higher consciousness forms? In the cases that have come closest to such a scenario, it does not unfold. Unfolding consciousness is just as dependant on the social structure that cares for it whether it be animal or primitive human.

So, let's go a little longer term. Would the generations of these people progress faster than what the world did? Here we introduce another variable: the environment. Are we talking Fiji or Australia for the island size? There is huge geneology project based on mitrochondrial DNA samples that tracks the so-called "seven daughters of Eve" as they spread out of Africa. What I noticed about the study that really wasn't the focus of the study itself, is that human consciousness deepens as people moved around more. The civilizations that stayed put more (such as the aborrigines and native Africans) had civilizations that retained their tribal nature (PURPLE in Spiral Dynamics terms) longer. Familiarity didn't spark innovation. But tribal members who set out for the unknown eventually produced civilizations beyond tribal associations. In short, if the island doesn't produce the opportunity for much exploration and variety, it is more likely to remain primitive.

There are, however, a couple of spiritual theories where this could provide n interesting analogy. Physics tells us there is a possibility of universes other than this one, one such theory being an oscilating universe that follows a series of Big Bangs and Big Crunches. In Hinduism, the universe is believed to be a series of inhalations and exhalations of Brahma. But it is not just the physical that is made and remade, information is also embedded into this fabric, sometimes known as the Akashic Records. So it is possible that our civilization has progressed faster in this universal cycle than the previous one, because we have access intellectual features already "thought up" that we just had to divine. This would explain why some people see innovation "in a dream" and just seem to "know" it is the right answer. Of course there is no way of knowing if we are still within the bounds of the last cycle of intellectual knowledge or if we are now probing new depths.

Finally, most religious systems that subscribe to some form of reincarnation say the Soul collects all wisdom from its incarnation and then uses that wisdom to select its next incarnation. It is therefore of utmost importance to collect as much knowledge as possible so that you continue to make choices that allow you to further your wisdom. In Plato's Republic, he describes this scnario in "The Myth of Ur". Sorry for rambling.
-TC