Its perhaps worth noting that the Soviet Yak-44 AEWC was designed to also operate from STOBAR carriers. That primarily explains its very impressive power figures. Not saying the same will be true for the Chinese aircraft necessarily, but just pointing out fixed wing AEWC does not automatically mean it needs a CATOBAR.
Yak-44 was to use propfan engines. Compared to turboprops, they have better speed and performance, with the same fuel economy.
This is the wikipedia article:
I dont think that china has this kind of technology. So, i assume that KJ-600 needs a catapult.