Answer by Jason Yeaman:
Some. Burke destroyers on point steaming with a SG or AG have a first responsibility to Carrier defense, but new C4I mostly allows groups to operate as a single organism comprised of smaller role-based components
However, in your scenario of a carrier being attacked from. All sides by subs..one would wonder where the hell are the groups own attack subs. And why the hell do surface combatants need to play torpedo sponge when the bubbleheads are supposed to have that watch.