It seems to behave like a verb, and would be the negated form of a verb あく if it were.
Yes, it must be, because it appears (or has appeared) in various inflected forms such as あかへん. There are multiple theories about where exactly it comes from, but according to 日本国語大辞典 it's derived from らち(埒)があかぬ:
Martin's Reference Grammar of Japanese (1975) is slightly dated but has some interesting discussion on page 385, including a possible alternate etymology from いかん:
The Kansai variant akan apparently is the result of assimilation of the first vowel of ikan to the second. Maeda 1965 accepts Ōtsuki's explanation that akan is a truncation of rati [ga] akanu 'makes no headway', but skeptical Yamanaka 1970 seems to have reached a conclusion similar to mine.22 Maeda says that in Ōsaka akan dates from the 1850s and appears also in the forms akahen, akehen, akimahen (an example appears in Tk 3.290a), akasimahen, akesimahen; he mentions modern "affirmative" formations in questions: aku ka akan ka, aku mon ka, aku ka i.
And here's the footnote:
22. We may be wrong. Miyara 1954.45 says the Nagoya equivalent of akan is datikan or datyakan, coming from rati-akanu.
This footnote does appear to support the same etymology given by 日本国語大辞典, but I think the passage from Martin's grammar is still very interesting because of the range of forms he reports.
Here are the full names of the references in the quote above:
- Maeda 1965 = 上方語源辞典 (前田勇 1965)
- Miyara 1954 = 風土と言葉 (宮良当壯 1954)
- Yamanaka 1970 = 方言俗語語源辞典 (山中襄太 1970)
- Ōtsuki = 大槻文彦 (1847-1928), in reference to his work 大言海 (I think)
- Tk = the writings of 徳川夢声 (1894-1971)
As you can see, Martin lists a number of interesting forms that it's appeared in, including unusual forms like あくかあかんか in which speakers are clearly treating it as a verb form.
However, despite these citations, あかん doesn't usually appear with a complete range of verb forms, so it's fairly unusual as negated verb forms go. I don't think the affirmative verb form あく would be understood in most contexts. By far the most common form is simply あかん by itself.