Yes, but CWIS isn't the only anti-air defense on a US Navy ship -- there's also the RIM-116 Rolling Airframe Missile, as well as vertically-launched anti-air missiles (RIM-162 Evolved Sea Sparrow Missile). CWIS is the weapon of last resort, after all of the other anti-air options have failed.

Additionally, ships are usually not alone. The other vessels in the battlegroup will also provide their anti-air capabilities. If they are with an aircraft carrier, then there are also planes to provide air defense.