I doubt if the J-10 airframe is suitable for a sea faring life. The pounding of arrested landings takes a toll on the best airframes engineered for sea duty. It takes a very sturdy and specially engineered airfame so an aircraft will have "Sea Legs".
From a design and engineering perspective, they could navalize the J-10 design.
It would require that they do a number of things and would not be the type of thing where they would retrofit older planes. They would have to be new builds.
They would have to do the engineering to allow for, and then build into the aircraft the following:
1) A strengthened undercarriage and landing gear that could take the pounding.
2) An arrestor hook and the underlying structure to handle the traps.
3) An exterior coating that was resistant to and protected the aircraft and its innards from the salt water environemnt.
4) Appropriate changes if necessary for refueling.
5) Adding, if necessary folding wings to minimize space.
If the J-10 met their functional requirements in terms of payload, function, etc., and was projected to do so for a couple of decades into the future, thenn it would be cheaper to do these things than to design and build another aircraft from the ground up. The question is simply whether this is something the PLAN feels would meet its requirements and needs.
If not, then there is no sense considering it. If so, then they will (if they haven't already) take a hard look at it.
Not every country ahs the luxury that the US does to have purpose built aircraft purely for naval air operations. Even the Chinese J-15 is a derivitive of their J-11s.
The US Navy E2-C/Ds, the US Navy A/F-18C/D/E/Fs, the US Navy EA-6B Prowlers and E/A-18G Growlers are all current aircraft that are purpose built for the US Navy for carriers (and used by the Marines there too). In the past, aircraft like the A-4, the F-8, the A-6, the F-14 etc were too. The A-7 is an aircraft that was designed by the Navy and then adopted by the Air Force.
But, in other navies, where they operate their own aircraft, like the French now, you have the Rafael serving both needs but a variant, the Rafael M for the Navy which is not just an upgrade. It is a seperate build. Like the PLAN, the Russians used a variant of their SU-27 and made it the SU-33. The new Mig-29s are a navalized version of their air force Migs.
Not many people operate their own aircraft off of carriers. MOst buy them from others. The UK will operate the JSF, which was built to serve the needs of all three branches and are different variants of the same aircraft.
Will the PLAN develop and ever use a navalized J-10? I do not know. I know they could if they wanted...but it would not be a simple matter of upgrading existing aircraft. They would be new builds like the J-15s are, like the SU-33s were, like the Rafael Ms are, like the Mig0-29Ks are, etc.