The question is quite clear, but in my personal case I want to emulate the greenish dot matrix screen of the GB in my game. Will this count as a color in my palette? I'd say that it shouldn't, as the green screen in the GB is not a 'processed' color, just the screen itself...

That's fine since you are trying to give it a more authentic GB 'feel'

Maybe have an option in your settings to turn it off if the player chooses too.

The "green background" in the GB is the lighter color of the palette. Other than that one it has another 3 colors

https://en.wikipedia.org/wiki/List_of_video_game_console_palettes#Game_Boy