Regardless of the RAE classifying it as an adverb, I would definitely go more with what Manuel Seco proposed in his Gramática Esencial de la Lengua Española, page 80:
The word "he" (as in "he aquí el resultado"), which grammars and dictionaries classify sometimes as "imperative of the verb 'haber'" and sometimes as "demonstrative adverb", is, in fact, a verb that is both defective (because it doesn't have all conjugated forms) and impersonal.
First of all, as Seco indicates, one has to understand that this "he" is not a conjugation of the verb "haber," but a verb all in itself, that is, "he" is not only a verb, but one without tenses, persons or numbers, therefore, "he" is the only existing form and that is why it is a defective verb. While this may seem a little strange, truly it is not. In Italian, for example, there is a verb ("ciavere") that doesn't actually exist which can be used in spoken language, but that should not be used in written language because no one has agreed in how it should be written. In fact, defective verbs are quite common.
Secondly, having "he" as a verb immediately vanishes all the struggling regarding its usage: both with clitic pronouns (e.g. "me", "lo": heme, helo) and with direct objects.
In his Diccionario de dudas (PDF file), on page 243, Seco expresses that "he":
[...] always has two forced companions: 1st, the adverb "aquí" ("here") or "ahí" ("there") (occasionally, another adverbial complement of place: "henos ya en casa" '--"here we are already at home"); 2nd, a direct object: "he aquí el resultado" ("here is the result"); "he aquí a tu madre" ("behold your mother"); "heme aquí" ("here I am"). It is mainly a word of literary use.
As seen then, by having "he" work as a defective, impersonal verb, both clitic pronouns and direct objects fit properly, just like with any other verb:
- He aquí las consecuencias de mi desidia.
- Heme aquí sin saber qué hacer.
- Hételas [ahí] todas desamparadas justo cuando más requerían de tu apoyo.
Back to the first quote, Manuel Seco then continues to explain:
The non-verbal origin of this word, an old Arabic interjection, which has fooled so many grammarians, is of no importance when it comes to defining it by its actual functioning in the language.
We should note here the "is of no importance" part, so we should not worry much about the origins of this defective verb. Anyway, as a brief cultural summary regarding the Arabic "hā" (ها) interjection, here are a couple of links that may be of interest: wiktionary, wordhippo. One may also check the Spanish "he" page.
For anyone wanting to practice their Spanish reading and improve their grammar and general knowledge:
ㆍespañol ㆍvocabulario ㆍgramática