There are teachers who teach an "intervallilc reading" method from the very start, so the idea that all notes are read individually at first is not strictly true. You do want to be able to recognize any note on the staff, coupled to its location on the keyboard, as a single reflex. In the case of your GBD, if in closed position, it will look like a snowman. Even a beginner will quick learn to recognize that is a chord reflexively. Or if you see a scale G, A, B, C, D, E, .... the row of notes will form a slanted line, with the notes alternatively going line-space-line-space etc. = interval of seconds. You need to recognize that first G, and you might want to notice where the scale ends. You're doing both and several things.
If you are already experienced with chords, then your pre-existing skill will also kick in.