Well, based on instances shown so far, CoC is a must for King of Hell to be named on an attack.
Take a look at this page. The first two instances have a lot more Ryo flow than Lucci's case and neither of them are KOH.
The panel on the bottom is KOH. The first two panels are just new standard to Enma's satisfaction.
There was even more Ryo release during Hiryu Kaen and it wasnt named as King of Hell because it lacked CoC.
Oden who had both wasnt able to pull King of Hell either. So even with CoC and CoA it is still not KoH, this is unique to Zoro.
I am willing to support your take as soon as we get an instance of King of Hell named attack without aCoC being present.