I don't know. The J-20 could still very well be just a strike fighter.
Chief reason being hamper by the technological bottleneck eg. super agility / super maneuverability - and so far there is no reason to believe China has the ability to make vector thrusting nozzles, and quality high performance engines and stealth.
Strike fighter on other hand, requires less sophiscation - its merely acting as launching platform for bombing/strike mission where it can launch its payloads (look at F-111, Panavia Tornado) and then bail out quickly. It doesn't need to be as maneuverable as air superiority fighter, and since it doesn't need to do dog fighting as much, stealth is not as much a requirement.
It all depends on the engines (VTC/high thrust), and the level of stealth J-20 has.
It took american almost 25 years to finally developed F-22, and before that, even though they categorized and gave F-117 a fighter designation, its really was a strike bomber. It was limited by the technology at the time, it could not fly at high speed and keep its stealth, and its maneuverability was limit by the aerodynamics of its airframe and underpowered engines.
So unless China can overcome those bottlenecks, it can call it air superiority fighter, but its real performance will say otherwise.