For PLAN assets to detect enemy warships within a few hundred KM or a PLAN SSK that asset would have immense detection and comm capabilities. Sub comm is mysterious and kept secret but assuming all that is achievable, what is this asset? High altitude drones or satellite most likely but what will guide those sub launched AShM? The SSK itself cannot guide them but they have had AShM capability for about 2 decades now so clearly there's some CEC. During this detection and CEC targeting phase, the USN will be working at destroying and blocking those assets and surface vessels. They'll be launching their own anti-sub attempts and it's all pretty difficult to keep the chain running for the PLAN. I would think those SSKs are more likely going to be launching torpedoes at those targets instead of AShM. The only case I can think of is some networked swarm/saturation attacks using AShM which means SSKs launching will add to those numbers. Presumably all those launching vessels are within range for AShM.
There are plenty of different ways for the PLAN to deny wartime access. SSKs are definitely the frontline and perhaps the most effective and threatening. The US will need to be conducting ASW while contesting surface, air, and digital domains and defending against direct attacks. Their answer in doctrine is air superiority and outranging everything while knocking each prioritised target down in a kill sequence. I'd imagine PLAN SSKs and China's resistance in the air are at the frontline of access denial. Those ballistic missiles and HGVs are more "assassin's mace" type weapons to add to the effort.
Traditionally subs needed to launch a comms antenna or surface to periscope depth to get radio communications. But there was an article posted on this forum a while back on an award being issued for a break-through in underwater radio communications, so PLAN subs may no longer need to do that and can get some comms while fully submerged. Unless I am vastly underestimating Chinese tech, and they have actually operationalised quantum entanglement communications, I think this will be a low bandwidth comms means, probably enough for text messages only, which would be enough.
Remember that the sub only needs to know what direction to launch the missile. After that it will be down to the missile seeker or an off board asset to datalink course updates to it.
This would be a new technology, because even though the PLAN has operated sub launched AShMs for decades, it is only in recent years that they have moved beyond the old sub launched C801/2, which only had a range of around 50km, which was most likely limited to such because they would have been relying on purely the missile seeker for guidance, so there would be no mid-course updates. Hence to try a shot like that from much further away would be too much of a low probably shot as the odds are good the target ship would have moved enough that the missile seeker won’t be able to acquire it once it has reached its initial launch target destination.
The kill chain for such a shot could be fairly robust, with AWACS, AEW drones, satellites and maybe even OTH radar and passive EW could all be capable of giving updates enemy fleet location data, that can be data linked to missiles for mid-course update.
You need to remember that one of a carrier strike groups primary defences is not being detected, which means very strict emissions management. Problem with that is that unless the carrier thinks it might be in danger, it will be limited to passive sensors, as blasting away on full power with shipboard radar is a great way to let the enemy know where you are with EW signals analysis.
As such, if it was a drone with passive EO sensors that spotted the carrier, it may not know that missiles are coming at it until the seekers on them goes active.
That is one of the key threats of lurking SSK with long range AShMs - they can threaten enemy fleets when they still think they are far from danger zones.