In English, does the subject-verb-object-adverbial complement modify the subject, the adverbial modifies the predicate, and the complement modifies the object?

That’s not the case. Attributives modify nouns. There is no obvious stipulation on what components they modify in the sentence, but they are usually used to modify subjects and objects.

for example: He is the man (hurt himself yesterday)This modifies the object the man

Michael, (playing basketball now), is my friend.))) modifies the subject .

Adverbials do not modify predicates. The role of adverbials in sentences is to supplement the explanation of the time, cause, result, location, etc. of something.

He left ((before I got up))He left is explained here.

Complements mainly supplement the components of the sentence, usually modifying the object, and can also modify the subject.

I appointed him ((((general manager.))object complement.