Circulate, no, diffuse, yes. The crud in the calipers pretty much stays there. Any moisture in the brake fluid will diffuse throughout the system. Water mixes with brake fluid and it can work its way in right in the strangest of ways. Through the rubber brake lines and in the master cylinder vents.
That’s why @rocketman suggests bleeding the system regularly. Get the master cylinder fluid to push the crud out (not back up into the ABS valves) and clean, dry fluid to take its place. If you are rotating the tires, bleed the system then. If you are changing brake pads, bleed the system then. Do it periodically as you work on other things and you’ll prevent a lot of internal corrosion that occurs if the fluid gets old and wet.