So the battle group has the ability to take out the search drone long before it could track the carrier,
Not unless the Aegis ship is well away from the carrier in the right direction. No Standard will get that far. Even the monster Typhon maxed out at 200 nm.
and should that fail, to take out the missile in the exoatmosphere, and if that fails to take out the RV at high and medium altitude inside the atmosphere,
Possibly, but the Navy's palpable nervousness about ASBM says that it's not a slam-dunk. And every BMD interceptor is one less SAM.
and should that fail, assuming it's a deck puncher, to take it out in the terminal phase using close-in defense systems.
Phalanx and RAM? GLWT, dude.
Sorry for being unclear - I was talking about a guided RV rather than payloads. Although once you have that, the exact damage mechanism is up to the user and is not a difficult challenge.