Yes, I do know comics. Which is how I know that in DC there is no distinction between a "divine blessing" and any other magic.
Magic is magic, where the magic comes from isn't relevant.
Do you know what stops Billy Batson from tapping into the power of the shazam transformation to cast any spell he wants?
Nothing but the wizard's annoyance. When the wizard dies and Billy becomes his successor he goes from flying brick to spellcaster.
Likewise, when stripped of his powers, Black Adam regained his powers from a spell cast by Faust, using Isis's body as his power source.
So magic is magic, and when they transform they are humming with magic.
Hence my comment that Adom's magic being theurgical shouldn't matter.
If the Danner formula gobbles up all available magic then the shazam transformation shouldn't be an exception.