Are the purest, most saturated colors (red, red-orange, yellow-green, blue-violet) the ones shown on the color wheel?

Yes. The fully saturated colors we typically see on the outer ring of the color wheel are the colors in their purist and most saturated form. They have no other colors in them except themselves. For example, cadmium red light is only cadmium red light. The colors found on the outermost ring of the color wheel can never be more saturated. They only can become less saturated as we add additional colors or black and white.