Coincidentally, I own an airsoft rifle with a red dot sight, and i did a practical experience of aiming down my red dot sight and focusing my eye focal depth on the crosshair while swaying my rifle around like crazy. But (logically) as the eye remains in exactly the same position in relation to the red dot sight, there is no motion blurring going on on the crosshair itself, only on the distant background behind it.
So to conclude, anything attached on the weapon including the red dot scope crosshair should not be motion blurred as long as you aim down the sight ;)