Does it save battery to have your desktop background set on a dark color?

Do you think that a laptop consume less power when the color displayed on the screen is darker ? (And even less when the color is totally black) ?

I don't mean reducing the brightness or contrast settings but simply have a dark blue or dark green desktop (windows background color), and that parts of this desktop is visible (Grrr)

No, because the LCD backlight is always on, even if all the light (or most of it) is blocked by the pixels in front of it (thus displaying black).

The newer LED-lit LCD screens could eventually save some energy, but not the side-lit LED screens. Check this out: Difference Side-Lit LED versus Direct LED.

As of 2020 the answer is sometimes, depending on hardware and what's displayed.

Laptops equipped with OLED displays will use less power when displaying darker content, because their pixels can actually be dimmed and thus use less power. OLEDs are rather uncommon in laptops, though.

Laptops featuring LCD displays can to some extent save power with dark content, as long as it's dark overall on entire screen rather than locally. That's because laptop graphics drivers can detect dark content and achieve more-or-less the same visual result by adjusting the contrast to be more efficient. The transition to and from this "dark content mode" is quite jarring though and may be unacceptable to some users. It's also not as efficient at energy saving as OLEDs. So in my opinion setting a dark background and theme just for battery saving is not worth it on LCD screens.