The greater capability of a larger airframe like Y-20 as AEWC for larger radar, or more command, or more fuel, is all there, yes.
The question is whether that greater capability is actually worth the development, testing and procurement of a Y-20 based AEWC, versus whether the KJ-500 solution is already sufficient for now, especially given the increasing trend of moving towards more distributed, more dynamic and more survivable AEW solutions into the future.
If KJ-500 is already a sufficiently capable AEWC platform, it may be more sensible to just continue buying them, and put money to develop and procure a more future proof and survivable AEWC solution instead.
Personally I am not sure what the specific correct answer is at this time.
What you are describing is basically a whole new aircraft.