I agree that I think at least one additional 003 would be built before they build their first nuclear carrier, for similar but slightly different reasons to you.
I certainly agree that 003 as a carrier seems like it'll shape up to be a very competent CATOBAR carrier and will be able to achieve many of the requirements that the PLAN has, however compared to a nuclear carrier, deficiencies in endurance, in capacity of aviation fuel, and slightly greater size and power output will still remain.
The reason I think they will want to build at least one more 003 pattern carrier, is because I fundamentally do not expect the first nuclear carrier to start construction until late this decade. 2028ish.
003 will be launched in 2022, and I expect the first nuclear carrier won't be launched until 2030 at the earliest, possibly even early 2030s.
That is nearly a decade between launches. For such a long duration, I certainly expect the PLAN to seek at least one more carrier, and an 003 pattern carrier (maybe with some small refinements) will certainly be appropriate for it.
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I agree. I probably should have added this particularly point in my post above. This was exactly the biggest reason I believed that PLAN should build at least two Type 003 even if the Type 003 turned out to be a 70,000-ton class carrier, if there would be some wait time before the CVN would be ready. The experiences and the availability that PLAN would gain by operating two CATOBAR carriers far more outweigh the deficiencies and additional cost of somewhat less ideal first-time CATOBAR carriers.