Yes, you are bringing Diurnal in part for their regens since they stack with all effects aside from the same from another Diurnal AST. It's a given that AST is neither a full-powered WHM nor a full-powered SCH, but the Diurnal HoT remains effective in all but one healer pairing.

As for 4-man content (any content, really), currently there aren't many reasons to take either AST over WHM or SCH, but we have enough threads about that.

I'm still baffled as to why anyone should want to pair a Nocturnal AST with a SCH only to cast very slightly stronger versions of Cure, Cure II, and Medica when you can bring Diurnal to do the same at a tiny bit less potency but with greater potency/mp over time with applied HoTs.

Haven't had the chance to test Noct CU with Soil, but that's because both are nearly useless except in progression. Even if they do stack, the only way anyone will care is if this allows a team to survive a HP check that is the only thing gating their progress.