Polynesia was probably added to the game because they are really unique. There's nothing even comparable to that part of the world at that point in time, ever.
Even though I can't imagine there were that are/were many Polynesians (or any oceanic people for the matter), their impact on American culture is really profound considering their small size. Just think of all the "Hawaiian" words in American English -- wiki stands out as do hula and luau. For the record, I'm not arguing that their influence on American culture makes them worthy of inclusion. Just that culturally powerful civs/people/whatever often leave their mark on others -- Hammurabi's code of laws anyone?
Anyways, I'm more concerned with the balance aspect. Their UA has two interpretations:
1. Units can enter water tiles and move across oceans/seas on turn one. The logistics work the same as any other civ that has researched up to astronomy -- meaning that the unit loses all movement points when it enters the water tile.
2. Units can enter water tiles and move immediately -- meaning that the unit does not lose all their MPs when they embark (and presumably disembark).
The first possibility could be incredibly powerful. Get the settler and warrior in the boat and find the new world (or settle one city in the old world and colonize the beans out of the new world). As others have mentioned, Terra would be unfair and pangea would -- well just don't pick it (sounds like the Ottomans).
The second possibility is cool, but not overpowered or lame (except, again, on pangea). It'd be especially cool on archipelago maps, or maps that have a Polynesian start-bias (start-bias would be must have coastal start, must have islands nearby). Yeah you could pop a lot of huts, but that's hardly a game changer. I'm more interested in the extra get-away movement points or, even better, launching a surprise attack from the ocean and getting to move one tile inland. This would make it so you could have two rows of units disembarking from the ocean, not just one -- meaning you could get your infantry off the coast and plant siege behind them in the same turn, instead of having to use two turns. I know this sounds insignificant, but after having played archepeligo maps, some invasions are near impossible without a massive fleet. This ability, if you can sneak it in right, would allow your army to establish a beachhead before the battle even starts instead of losing units due to an entrenched enemy and ships "snagging" your embarked armies.
Also, and I'm sure someone pointed this out, the statues are a tile improvement. I know this because of the art-style the icon uses at the leader-start page. The only other civ to have that style of art for one of their uniques is the Incan.
I'd be willing to bet it's +1 production to adjacent water (non-lake) tiles. So, the statues would be a trade-off. You get increased water tile production, but you have an "improved" tile that isn't improved at-all. On the combat-side, they provide a small combat boost (enough to negate being on a flat, non-marsh tile).