Can he be an object pronoun?

He is a subject pronoun in Who is he? The question has subject-auxiliary inversion; it it asking the listener to fill in the blank in the corresponding uninverted statement He is [noun phrase]. E.g. "He is [my brother]" or "He is [the friend I told you about]." It's the same sort of structure as Where is he?

A piece of evidence that he is the subject is that when the pronoun after the auxiliary verb changes, you have to use a different form of the auxiliary verb: Who are they?, Who am I? English verbs agree with their subjects.

Firstly, and to answer your question, the verb to be has historically used what is called a "predicate nominative" when it needs a second object. I say "historically" because constructions like "It's me!" or "That's him!" are becoming increasingly common, but in this case "Who is he?" and similar questions have retained the predicate nominative. This is why both "who" and "he" are in the subject case.

Secondly, questions like this do not have implied subjects. The subject of the question is "who", which you can see because it is in first position and a noun phrase (specifically, a pronoun), and the main verb - not the auxiliary! - is "is". The only (prescriptively) grammatical sentences with implied subjects are direct commands, with an implied "you" in the (empty) first position, but I'm getting off topic.

I recently read that the question of the subject of a sentence that starts with a "wh" word was controversial, so disagreement on it is probably quite normal.

The one point where I think there is clarity here is the correct form of the pronoun "he".

Pronouns in English decline just like all verbs in German and Latin. This means that they take different forms depending on how they are used in a sentence.

"He" is the nominative case of the pronoun here. The nominative case is used for pronouns in two positions: as the subject of a sentence, and as the predicate nominative, which follows an intransitive verb -- in this case, "is". Intransitive verbs are verbs that don't take a direct object -- objects that are not directly acted upon through a verb.

"Him" is the accusative case of the pronoun. It is used when the pronoun is the object of an action verb or a preposition -- "I saw him", "I gave him this" ("this" is the direct object here, while "him" is the indirect object that follows the implied preposition "to") , "this is for him". It is not used with an intransitive verb.

It's true, as @No Name mentions, expressions like, "It's him" are used frequently. Technically, however, the proper form would be "It's he". Once in a while, people do use this form, but I think it's become increasingly rare over the years. Nevertheless, it's the grammatical choice.

I hope that answers your question, at least the part about the role of "he" in the original sentence, and that it's helpful.