While it is certainly possible to navalise the J10, and there have been several examples of Air Force fighters being re-engineered for carrier ops in both east (Su33 and Mig29K) and west (F18). However, it is a formidable engineering challenge nonetheless, which will take many years.
Looking at all factors, there are many reasons which leads me to seriously doubt if there ever will be a naval J10.
1) Safety. For naval operations, twin engined planes offer a degree of redundancy and security that a single engines bird simply cannot match.
2) Growth potential. While the J10, and especially the J10B is a fine fighter, which should be a match against anything that isn't 5th gen, the fact remains that the J10B pretty much represents the ultimate evolutional potential of the basic J10 airframe. When most first class carrier operators are moving onto 5th gen designs, the J10B would simply be outclassed by the F35 and J31.
3) Timing. Had the PLAN carrier programme kicked off 10 years earlier than it did, a naval J10 would make perfect sense. But as things stand, its just too late for the J10 to get in on the carrier game. By the time a carrier J10 is operational, most other carrier operators will be fielding F35s rather than F18s, Harriers and Rafales, and even China's own J31 should be nearing IOC.
You should also consider the PLAN's own timetable. I mainly expect the next 5-10 years to be a time of learning, test and foundation laying for the PLAN carrier programme. During that time, the PLAN will mainly be concerned with playing catch up in terms of knowledge and experience in carrier operations and design rather than trying to build up a massive carrier force. I expect the first indigenous carriers to be built, maybe with two different classes of medium sized conventional carriers, but I do not expect the carrier fleet to get beyond 3 or 4 unless there is a major escalation of tensions and war looks imminent.
For a carrier fleet that size, it does not make sense to have two manned carrier fighter types as you are looking are barely more than a hundred carrier fighters total. Investing all the time and resources into navalising the J10 only to build 50 planes is just not worth it, and I don't think the PLAN will want to settle for two conventional types as its only carrier fighters for the next 20 years. It would be willing to have one conventional type if coupled with a second 5th gen type, but not two conventional jets and no 5th gens and three manned carrier fighter types could just be too much of an overlap.
I do not expect the PLAN to start a serious quantitative push on its carrier fleet until 10-15 years from now at the earliest, after it has had a chance to get a good grounding on carrier ops, carrier designs, and have moved onto nuclear super carriers. Incidentally, China should also overtake the US as the world's largest economy around then, so China would no longer be worried about getting sucked into an arms race with the US by then. That is plenty of time to get a medium 5th gen carrier fighter operational if they start now.
3) Workload. CAC is currently spread pretty thin with the number of major projects they have running, in 5-10 years time, many of those projects would have come to fruition or moved into the later testing stages, freeing up key personnel and assets to start the serious work of prototype production and flight testing for a new fighter.
4) Coporate strategy. As I have already touched upon above, it is a little too late for CAC to get in on the carrier game with a naval J10 proposal. Rather than waste time and resources trying to compete with the J15, which is likely to only have a limited production run, it would make far more sense for CAC to just concede the first round to SAC and start fresh with a design to compete for the carrier 5th gen contract, which is more realistic time wise, and have a far bigger probable production run.
It makes little sense for CAC to start from scratch now trying to compete with a design that is already nearly operational deployment, for a relatively small production run, especially when it is so busy now, and even more so when doing so would seriously undermine CAC's ability to seriously contest SAC for the far greater prize of a carrier 5th gen since SAC is already ahead there as well with the J31. CAC would be playing catch up already against the J31, it simply cannot afford to waste time with a carrier J10.
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