Not exactly, there are a lot of different kinds of displays and depending on the implementation they may or may not consume less energy depending on the comulative brightness of all the pixels. Even LCD panels nowadays have what's known as "dimming zones" sometimes, which is basically instead of using one huge light behind the pixels uses a matrix of smaller lights and can dim the lights behind darker areas that way, which leads to less energy consumed. It's mostly used for HDR instead of energy saving, though.

But in general the idea is correct: not all displays will consume less power in dark mode, a lot of them will blast the backlight anyway and block the light with the pixels afterwards, actually resulting in your display being heated a bit more than when using light mode.

A more important point is whether it works or not, displays make a very little portion of global energy consumption and whoever is trying to make you feel better by using less energy with your display is just trying to lead you away from taking actual action against people actively trying to extract all the possible value out of our planet.