They'll navalize the J-11, since it's essentially an SU-27 Flanker, which has already been navalized (called an SU-33 Sea Flanker). The tech already exists and the ChiComs aren't much for innovation. Which is why they bought the Varyag in the first place.
It means that the Chinese will be able to project power in the Spratlys and have a domestic source of oil, which is more of a problem for the Vietnamese than it is for us since the Vietnamese also claim the Spratlys. Military forces of Malaysia and the Philippines also occupy various islands in the chain, so it could be a free for all. Brunei is also getting a little nervous as well, I imagine. The Aussies will be sorry they decommissioned the Pig, now.
The Varyag looks big, but it is surprisingly anemic in capacity and capability. It's sister ship, the Kutsenov, can only embark with two squadrons of aircraft, at only 12 aircraft per squadron, plus helos and ancillary aircraft. That's 2 dozen combat aircraft. Ours carry about 90 aircraft, but realistically, even we have fewer embarking now.
Something else to think about, the Russians are going to be completely refitting their one big-deck carrier, decommissioning the Sea Flanker, and going with a navalized version of the MiG-29 Fulcrum. Reason being, the Sea Flanker is a fighter, a big one. It can engage aircraft, but lacks any kind of air-to-ground capability aside from unguided weapons like dumb bombs and rocket pods, no air-to-ground precision-guided munitions and no capability to guide them. There was an upgraded version offered to the Russian Navy, but they still bought the Sea Fulcrum for yet another good reason...it was cheaper. Sukhois are expensive.
The Chinese have, at the last time I checked, about 7 carrier-capable fighters.
Is it something to worry about? Yes. Especially if our beloved president decides to buy off the Chinese with technology to keep them servicing our debt.