Not a chance in hell. "Converting" a STOBAR into a CATOBAR involves far more than putting cats into the flight deck. It would involve deleting massive amounts of space currently being used for something operational and installing all the necessary power generation, storage, and transmission equipment in their place, not just the cats themselves. It would involve massive modifications of the flight deck, the 03 deck, and several decks below the hangar deck. The space and cost requirements would certainly be prohibitive. Any PLAN official foolish enough to even consider it seriously should be straight up fired.
Unless they actually planned ahead and already built in the upgrade options into 001A, much like the RN QE class.
Converting the Liaoning would be a massive undertaking, but then so was fixing her up in the first place.
And money is not the only consideration in terms of determining the valiabiliy of projects. Time would also be a massive consideration.
No matter how extensive the modifications needed are, converting 001A or even the Liaoning to CATOBAR carriers would still only take a fraction of the time it would take to build a brand new CATOBAR carrier.
If the security situation continues to worsen as the overall strategic rivalry with the US intensities, the PLAN top brass may well feel that having 2 more CATOBAR carriers operational after 1 year of upgrades and refits would be better than waiting 2-3 years for brand new CATOBAR carriers to be built. Especially once the naval stealth comes online, which will be a CATOBAR aircraft to be sure, no matter which design the ultimately go for.
Such an upgrade may well happen sooner than people might think. After the first two CATOBAR carriers are operational and the second pair of CATOBAR carriers, which will almost certainly be CVNs, are handed over would be a good time.
The crews from the Liaoning and 001A could transfer across wholesale to the new CVNs to bring them online in the shortness time possible.
The Liaoning and 001A could go straight into the same drydocks that just built the new CVNs; while the first pair of CATOBAR carriers take on extra training responsibilities to train up replacement crews for the Liaoning and 001A.
As such, the PLAN could potentially surg up to 6 combat ready CATOBAR carriers as early as 1 year after the CVNs are handed over.
Now ideally they could want to take things more slowly, but that is certainly one option, and a scenario where upgrading to CATOBAR would make a lot of sense.