Here’s the same colorway in a pair of socks (approximately a women’s US size 7 1/2); due to the size of the socks the colors produced thin stripes about two and a half rows wide. The Sweet Tomato heel makes an interesting cat’s eye shape as you do the short rows.
Last but not least is a pair of small square swatches knit up for a machine-washing/-drying experiment, the results of which are a post for another day. Just due to their size, the colors aligned apparently randomly.
So in these situations, three-color colorways don’t pool, but as always, your mileage (and yardage) may vary.