Why doesn't anybody ever ask the sailor?
In your case, the anchor isn't very likely to be down. Anchoring is a purposeful operation. Abandon ship is a different one. They'd have to have been at anchor first. Also depending on the nature of the emergency, they might have attempted to scuttle the ship, a process of self destruction which leaves classified material destroyed and the ship 100% unusable - every critical system would be hopelessly damaged, usually right around the special, hard to find parts.
I can say without a doubt in my mind that the hull can last for countless generations, especially if the ship isn't moving under its own power. The reason hulls have to be maintained is because you are pushing a piece of painted steel through the water at (nautically speaking) high speeds. This is an incredibly erosive force. Sitting (maybe at anchor) for centuries is nothing compared to that, even if the thing is getting hammered by hurricanes.
The barnacles would be obscene and it would need a serious amount of work to restore its original performance at speed, but it wouldn't rust through just sitting there. Even after the paint finally gave way and rust eventually set into the (rather high quality) steel, rust doesn't rust once it rusted. Something would have to physically remove the outer layer of rust to expose new metal to the sea. I have no doubt that the ship itself will be ran aground by prevailing currents before the hull simply springs a leak from sitting too long.
Now, a carrier group has lots of ships in it. If every single sailor in every single ship bailed out, and none of them were properly set at anchor (I'm telling you, this takes planning), the thing that's going to sink these ships is them bumping into each other. Eventually they'll bob up and down against each other's hull a few times, and eventually the damage will be severe enough to make the ships take on water - and then down they go. This scenario wouldn't take that long - unless they drift apart, this could happen in a few weeks to a few months depending on conditions.