Man I hate puns.
Anyway, I don't see the PLA-N sorting out many of their woes to a satisfactory level any time soon, right now they have malfunctioning submarines, inadequate air defence, as OOE pointed out the closest thing to a carrier they have lacks propulsion, insufficient amphibious warfare capability since the biggest external role of the PLA is to invade Taiwan if they act up. The entire PLA is having these problems.
In short, they're in a lot of trouble and they'll have to wait until the country gets a lot richer before they can really become a Military Super-Power.
And what good is a carrier if they dont have the air-defence Destroyers and anti-submarine Frigates to protect it?