Not necessarily for both. If China's other forces including carrier escorts are already on par with the competition, if it has a clear desire or need for action specifically with a carrier, then its carrier program would neither have a "sitting duck" nor a "white elephant" phase.
Even USN carriers could be killed with the right assets, skill, determination and a little luck, doesn't mean they are sitting ducks.
Even today, there are precious few forces in the world that could expect to be able to reliably punch through a PLAN carrier task force's defensive screen to take out the carrier, and none who can expect to do so without serious risk of taking significant losses to achieve such a kill.
As the PLAN develop and modernise, its fleet will only become more powerful, and its carriers better protected.
No one, not even the US, could go from no carriers to having a fully operational carrier fleet overnight. Crisis does not give you advanced warning, so you need to be ready at all times.
Its basically the entire principle behind all defence spending - you need to develop and maintain the capacity and forces necessary to counter and address likely crisis scenarios without needing to tell invaders to come back in a decade when we are ready.
If one were to take the view that unless you need it right this minute, its a white elephant, than all defence spending by nations not actively engaged in wars are white elephants.
Every time in history when the Chinese (or anyone really) neglected defence spending, they paid for that lapse many many times over in blood and suffering and death.
Not only are these low intensity scenarios hypothetical, China also has a demonstrated history and a continually voiced desire which is at the level of strategically choosing not to conduct such operations.
All crisis and calamities are hypothetical until they happen for real. When that happens, you are either ready for it or you are not.
As Chinese assets, interests and nationals are increasing going global, so must the PLA in order to be able to safeguard its overseas assets, interests and nationals. That is the key driving factor behind the PLAN modernisation in general, and its carrier programme specifically.
Carrier operations are also not the only way for China to take such action if it suddenly does an about face. It has LPDs with rotary air assets, destroyers with stand-off missiles, marines, special forces,
Carriers are far and away the most effective, flexible and useful tool for power project and expeditionary ops. Having one would allow the PLAN to conduct operations simply not possible without it and make all the other assets you mentioned far more effective in such a role.
and friendly-enough nations who are likely open to Chinese forces transit, short, or even long term basing for the right price.
Its never ever a sound policy to count on someone else doing you a favour.
