In some cases...very bad stuff. Remember, the Polynesian polities are on islands, and not always big ones, so we may see overpopulaton, warfare, and environmental collapse followed by population collapse after maize is adopted.
Some islands may avoid that, with the higher populations leading to the creation of centralized states that are able to maintain order and preserve the environment-for example, the Chief declares that the largest grove of trees on the island is his sacred grove, and so keeps them from being chopped down.
I actually don't think maize would be a permanent major crop in the Pacific due to the fact that it's not very drought resistant. You may get a scenario where maize becomes the crop of choice, the population booms, a mega El Nino effect occurs, the population drops and switches to manioc and then recovers but keeps with the more drought resistant crop.