China theoretically can leave a carrier in flames. But some prerequisites need to be met first. I am not sure how they're realistic to expect in a full blown us-china war. anyway, prerequisites, as i see them, are these:
cbg must be sufficiently close to china/taiwan so its carrier air wing can attack land targets and provide air cover. Otherwise, what's the point of having a cbg, except to launch cruise missiles? This prerequisite is probably most realistic one.
Secondly, it must be a lone cbg. If there are two or even more cbgs operating close enough together that they can offer each other protection, situation becomes way harder. Same goes for the vicinity of okinawa USAAF base with f15s to the said carrier. Though, the difference really is just in number of weapons china would have to posess/use, number of units it can coordinate, and of course number of lives it's ready to lose.
thirdly, china must be able, and this is most problematic and probably most unrealistic of three, to mount the attack without sufficient warning for the us to get help outside combat theatre and even, if they see a serious threat coming, turn back and try to get out of range. At sustained 30 knots, it could get even out of chinese aircraft range if the warning was early enough, i'm talking hours here.
Of course, zero level prerequisite for all this is location of the cbg. With satellites and enough forces (sea and air) commited to it, knowing it's somewhere in range of china, it's doable, albeit with probable high casulties in recon aircraft, etc.
So how would such an attack go? Main issue i see is number of extended rabge standard sm2 missiles in the cbg. would, for example, all 96 vls canisters of an flightII Burke class be armed with standard missiles, and how many of them would be extended range? Now how many burkes and tico would be in a war situation cbg? 3 cruisers and 4 destroyers seem possible.
So, assuming the cbg doesnt have time to flee out of range, an attack with huge number of aircraft would be one way to do the mission. First the forward e2 would need to be taken care of. That's many chinese fighters fighting through its fighter cover. Then the interceptors scrambled from the carrier would need to be neutralized, that's even more fighters. and i'm talking about large numbers here. assuming like 2 chinese craft for each superhornet (if chinese can do it on one for one basis, good for them, im not saying thats not possible) so that losing some 80-90 j11 planes. alternatively, you could send crap planes to get hit first but that'd mean like 300 kills for the hornets before they deplete their AAMs. but hey, if PLAAF can persuade their J6 pilots to go on such a suicidal mission, it's certainly a valid tactic but wasteful, as those crap planes are much better to be play cannon fodder a little later.
If there's any forward patrolling burke, that's taken care of too, with sub launched, awacs data navigated antiship missiles, to stay out of range of standard missiles. I am, though, prone to thinking that there'd be no forward burke, seems to be too costly a tactic.
So anyway, china needs to launch missiles now. how? thats where cannon fodder comes in. you make the cbg spend its extended range sm2 on a mix of obsolete j5, j6, drone aircraft, etc. i'd say its even possible, once the final route it set, to eject from the planes and just send em on autipilot to be brought down by sm2. of course we're talking here about huge amounts of aircraft to be sacrificed, hundreds of planes.
alternatively, the already mentioned sub launched antiship missiles guided from awacs that are outside the sm2 range could help but problem there is there's just not enough subs that can launch those in chinas inventory, even if there is enough missiles. maybe if there's 300 km range air lanuched missiles to aid them, maybe such an attack would be possible.
but to get back to the 'extended range sm2 depleted' scenario. carrier has no aircraft left to send, chinas planes get in range and launch a sufficient number of missiles. the end. Only left question there is what is a sufficient number. no one can tell that for sure. perhaps it could be as little as 50 or as high as 400. ive done some calculations, based on speed of missiles, range of usn defenses, etc, a 200 missile attack seems to be enough to take care of the majority of cbg.
But lets get back to real world. It'd take vast amounts of weapons, huge number of planes of which most would never return home. plus the ability to coordinate such a huge attack. Basically, it'd be something hard to repeat. maybe one more, tops, before even china runs out of resources to do it. And what then, even if it destroyes 2 USN cbgs within weeks US will send more.
*warning, crazy 'what if' scenario following*
IF china is to use the cannon fodder, suicide attack, saturation of enemy defences tactic, i'd suggest custom made planes. they need to be pilot driven in order to keep the price down and perhaps more importantly, to avoid jamming/decoys etc. but instead of asking of already trained PLAAF pilots to sacrifice themselves you make a call for ppl ready to give their life for a greater cause. with such huge population pool of poor ppl in rural provinces, it'd be easy for china to train such suicide pilots perhaps even in thousands.
next step would be designing and builidng a cheap plane in vast numbers, again, little under a thousand needed for one cbg attack, even if ALL the missiles USN can use in a few hour period hit their target. small prop planes are commercially sold in us for 18 000. chinese could manufacter such a plane for half the price, given the massive numbers produced. but since it'd have to be fast enough, simple enough, 1000 km one way range plane lets double the figure and multipy by 10. 360 000 per plane. that's 360 million dollars. enough money left to pay the families of the deceased for years.
Oh yeah, once the awacs planes have given them last known coordinates some 300 km away, a small number of the 1000 armada would have their own sensors, flir or such. it'd make them more expensive but only a small number is needed scattered among the 1000 strong force. that'd be enough navigation to find the exact location of the carrier force in those last 300 km (given the speed of planes) and the rest could just go where the planes with sensors tell them.
okay, granted, such an attack (im envisioning ramming the planes) would most probably not sink the carrier, but it'd damage it sufficiently it'd take a year before it can be put back in action. also, chinese would have to have enough of a grasp on their own airspace so those planes dont get attacked and destroyed before they're in air and enroute to the carrier. you can keep em outside even, dispersed enough. if US wants to waste a half a million $ missile for each such plane, let them.