Yes it looks like it.
Basically if the Apple IDs are part of an iCloud Family you can set up the kid's screen time from your phone, allow or block access to certain apps, set the downtime hours etc...
I guess that it's like when the kids request to buy something on the App Store, the organiser of the family and the other parent/guardians get a notification to approve the purchase.
EDIT :
I am the iCloud organiser of the family and everyone in the family is set up as Parent/Guardian so I decided to add my old Apple ID that is running on my iPhone 6.
The old Apple ID is set up as 'Adult' only and is the only one that appears on my iPhone X in the screen time menu (see the attached screenshots). The only problem is that info don't get retrieved from the iPhone 6 to the X. The menu stays blank like that.
But I can modify Screen Time's settings of the iPhone 6 from the X.
So I guess it shouldn't be different if it was a child's Apple ID. (minus the bug of course)