I'm skeptical.
China's doesn't have a nuclear powered carrier yet though is building one (Type 004). https://en.wikipedia.org/wiki/Chinese_aircraft_carrier_programme
Seems like it takes 12-18 months to complete a container ship once started. I don't think a prototype/demonstrator has been made and it seems they want to use a new thorium Reactor model which has only been deployed a handful of times and is not likely to be easy to make/deploy quickly in new domain.
Building a nuclear powered aircraft carrier will not resolve this question methinks.
They are in early planning stages for a nuclear powered tanker, but it is far from certain that they will even begin to build it. For reference:
Project Name: KUN-24AP
Project owner: Jiangnan Shipyard, China State Shipbuilding Corporation (CSSC)
Source: https://medium.com/the-dock-on-the-bay/china-to-build-a-thorium-powered-nuclear-reactor-07d9627b35ab