The USN has an excellent damage-control record, comparred to, say, the Japanese in WW2 was terrible at it.
I'm not convinced that PLAN subs with torpedos is going to be able to stop the USN. Even if they get lucky and "mission kill" a couple, the USN has 10 more to send.
If I were doing the planning for PLAN subs, I'd prolly allocate more funds toward SSBN's and SSG/SSGN's. The US doesn't have "no first strike" policy, so the PRC can only hope to deter the conflict from going nuclear with true MAD capability. A fleet of 8-12 SSBN's, each armed with 16-24 SLBM's with MIRV warheads, would offer that level of MAD deterrance by sea. For the PLAN to hit a USN carrier and cross their fingers in hope the US wouldn't retaliate is sheer folly.
For sinking a carrier at sea, I'd go with SSG/SSGN's. The USN Ohio-class SSGN with 154 missiles is a good example. They replaced each SLBM with 7 x Tomahawk missiles.
The new Type 94 SSBN is said to carry 16 x JL-2 SLBM's. If each SLBM is replaced by 6 AShM's, that's 16 x 6 = 96 missiles. Borrowing specs from the 3M-54E1 specs, each missile has 300km range and carries 400kg warhead. If the SSGN is able to fire its 96 missiles payload at distance, you only need a small % to penatrate the defenses and score a hit. Something on the scale/size of a 100,000 ton super carrier would prolly require multiple hits to disable it.