They would have not been able to mount a second strike and would have been effectively destroyed if not annihilated. If a missile trap is set so that the regiment is climbing to launch altitude over a missile ship it doesn't know about until the radar comes up and missiles start impacting, the fight will be over before it barely starts. So it was critical for the target to be identified and located prior to the regiment being committed. This takes time and allows the CV time to maneuver, set decoy groups, missile traps, fighter ambushes, etc. So the trick is to prevent identification and localization of the force.
Decoys run out and radiate.
Aircraft launch on missions running silent, fly out to a deception point at low altitude, then climb and radiate as normal. This is particularly effective if the first launch of the day locates a large, neutral merchant or cruise liner and everybody uses that as the reference deception point. Then the searchers actually see a target at the point that the flight patterns indicate. In wartime they commit, they lose their regiment, and the CV then has a free ride. We would also deliberately provide a false contact reference.