This article looks at the new Chinese carrier.
Aside from whether sea control missions should rely on carriers any more (and the debate over carriers should not mix up apples and oranges when discussing their roles), I suspect the Chinese could use their inferior carriers to conquer Taiwan:
China's first carrier was for studying and training. China's true carriers will be Chinese designed vessels. Those China probably wouldn't risk. But the old Varyag? If I was in charge of the PLAN (People's Liberation Army Navy), I'd dangle that carrier and some escorts northeast of Taiwan. As I noted, its presence would give us pause. And force us to approach more cautiously.
The final contribution of that first Chinese carrier to delaying our intervention could be to tempt us into taking the time to set up and execute the perfect naval strike mission. Sure, having sovereign pieces of US territory that serve as power projection assets is useful. And the Navy trumpets that mission in budget battles. But the Navy--deep down--wants to exercise sea control and take down another navy that tries to wrest it from us. It would be the best SINKEX, ever.
The Chinese just won't care if they lose that first carrier task force if the end result is that China has control of Taiwan.
Remember, China doesn't have to defeat our Navy (and Air Force). China just needs to hold us off long enough to defeat Taiwan. That's a big difference. And the Chinese don't have such a huge attachment to their carriers as we do for ours. We may feel good to sink a carrier with carrier air strikes after so many decades have passed since the glory days of 1942-1945 in the Pacific.
But China will give us that good feeling if it buys them the time they need to conquer Taiwan. And they'll still have their home-built carriers to build a blue water navy that will be supported by air bases on Taiwan province of the People's Republic of China.
The Navy might be so mesmerized by the opportunity to relive their glory days of the Pacific theater in World War II that they'll take their eye off the ball.
China would totally sacrifice inferior carriers, most important as stepping stones in construction and training to more capable carriers in the 2030s, if China can gain their most core of core interests in the face of American opposition.