In Japanese grammar, adverbial noun(副詞的名詞) often refers to conjunctions to make an adverbial clause/phrase with a modifying verb, adjective or clause, e.g., ところ, ため, 限り or 途端. It's not so commonly used, though.
全部 is an adverb in your example sentence, and a noun in, for instance, 私は全部の平仮名が読めます. "All" is an adjective in "All the people are happy", an adverb in "I'm all wet", and a noun in "I lost my all" also in English, no?