Oh hell yeah
Thats what lead Britain in the direction of building two full-size carriers. CIWS is indeed "too close for comfort." And even if Phalynx/Meroka/Goalkeeper gets the missile (which it will/does) theres still explosion damage. Kinda like Patriot which "hit" the SCUDs, but the warheads and other missile pieces still fell to earth and caused death/damage/destruction.