No, color palettes cannot be copyrighted in general terms. But there are some specific situations where this isn't the case:
One can copyright the arrangement of specific colors in a particular configuration (meaning the exact or near-exact positioning and arrangement of the colors), such as ColourLovers' copyright system for their palettes. This is essentially the same as copyrighting a finished work.
A business can copyright colors and color combinations for their brand but only for similar products when using a non-functional color (an example of a functional color is green for lawn products) if the public strongly associates the color with the brand. One example is as follows:
Owens-Corning launched the "Think Pink" campaign for its fiberglass building insulation. In 1985, a U.S. Court of Appeals in Washington ruled that the company had the right to prevent others from using pink for insulation.
Pink insulation is a good example of a color that is protected by trademark. When consumers see pink insulation products, they know it's Owens-Corning. The color pink doesn't symbolize anything in home construction. In fact, it's not even a very masculine color.
Pulled from this Color Matters article which has more information about the subject.
In essence, law tries to prevent products/companies from confusing users that it is the same as other products/companies when the color(s) is not related to the usage of the product.
But in some cases businesses fail to get their colors trademarked, it depends on what the government decides on a case by case basis.
For more information about color trademarks, the Wikipedia article on the subject is not a bad reference.