No, normal monitors use additive color mixing, but dithering isn't additive, it's averaging. With just red, green, blue, black you couldn't dither cyan, magenta, yellow, white, just some much darker versions of them. E.g. you get grey instead of white.

You can check this by trying to dither a full color image in a program like Photoshop. It doesn't work unless you use at least the 8 colors.

In fact, ink jet printers do something similar: They use subtractive color mixing to create red, green and blue dots (in addition to cyan, magenta, yellow and black ink and white paper), then all the remaining shades are dithered from those eight colors. It looks something like that: https://as2.ftcdn.net/v2/jpg/01/88/80/47/1000_F_188804787_u1... (though there black is also created with subtractive color mixing).

The color mixing type used by dithering is sometimes called "color blending". Apart from dithering it's also used when simulating partial transparency (alpha).