I remember trolls are made to design the house the drones build for them, because of prepping for the game, but do they have them do it as wrigglers? I just can't imagine going up to a baby and like "here, a pencil, draw your home"

They design it as soon as they emerge from their trials in the brooding caverns   and are picked by their lusus. So no, not while they’re wrigglers.