Sure, but unguided antiaircraft fire tops out pretty low in effectiveness, and aircraft are dangerous to battleships out of all proportion to their size, quantity, and cost - even if you shoot down ninety-eight out of every hundred, the two you miss can still achieve a mission-kill, if they don't sink you outright. And you'll never shoot down anything close to that proportion.

Battleships sided aircraft carriers for two reasons: one was to thicken their inner defense ring a little, and the other was because battleships alone, without a friendly air wing to keep the other side's strike aircraft away, were doomed.