See, my opinion is that they won't have a "vessel borne nuclear reactor adequate for a carrier" until they have a vessel borne nuclear reactor adequate for a carrier. I think trying to operate so many different types of carriers will be a real training/logistics/operational hassle in the long run, and it's better to just bite the bullet early and build a CVN with enough modularity to accommodate upgrades later on.
It seems to me that our major difference is in our perception of where China is at in terms of being capable of building nuclear reactors for carriers. I believe that they are fairly close already, and here's why:
First, China should have the technical know-how by now. I mean, after all, USS Nimitz was constructed in the early 70's, and China has operated nuclear powered vessels before, even if the reactors used on SSBN's are very different. So the problems remaining are political will, money, and time. The first two probably aren't of much concern, so it's really just a matter of time. Now, a CVN is tough to build and it takes a lot of time and experience to perfect, but it's something that even you and I understand so I'm sure the PLAN understands as well. Since it's safe to assume that the PLAN have always planned to eventually operate CVN's, I think it's also safe to assume that they've long begun to work on building nuclear reactors for them, especially since they know that they're in catch up mode and any step skipped is a step closer to their goal of catching up.
Now, have they put in enough time yet? None of us knows for sure. But if planning is adequate, then it makes perfect sense that they do not need to test out CATOBAR operations before building a CVN.