I think the Nuclear reactor is under the water line. So a missile hit would have to hit it at the right angle to damage and go through several armored bulk heads to get to it. But since we are talking what if...
A hit that damages the nuke reactor will certainly slow down the carriers operations. Remember there are two reactors per Nimitz class. If both go down, there are still back up generators to at least move the carrier to safety.
Something the size of a Nimitz, with over 1500 water tight bulk heads, will take a long time to sink. The IJN Shinano (70,000 ton carrier) took about 5 hours to sink from 4 torpedo hits and this is without watertight doors on its bulk heads. Your best lucky hit is to hit its munition storage. However, given the size the carrier relative to its munition space, it may not be more than just mission kill it. If such a hit can make an out of control fire, then the ship may have to be abandoned.