tl;dnr: Yes, it is possible that Aldo Gucci may have sold fake Gucci products on the black market in the 1980s, but cannot be verified as historical fact. However, it is a fair, if not fully explained with context, representation of the decline of the Gucci brand from the 1980s-1990s.

For this answer, I am citing Sara Gay Forden's The House of Gucci book, the primary basis for the movie, as a source. The book was initially published in 2000, about 21-22 years ago, and I have since noted several factual errors within the book itself that should be revised and corrected in future editions. Therefore, even though Forden tried to be as accurate as possible in writing the book, she also relied on a lot of third-party testimonies, as well as specific individuals who had issues with the Gucci family, some of which later turned out to be not accurate.

Others - such as Sheree McLaughlin Loud, an American model who is briefly mentioned in Forden's The House of Gucci book, and who dated Maurizio Gucci from about 1984 to 1990, declined to be interviewed by Forden for The House of Gucci book. However, after the publication of The House of Gucci, McLaughlin Loud changed her mind, and decided to be more open about her dating history with Maurizio Gucci. However, unfortunately, because McLaughlin Loud had declined to be interviewed by Forden for The House of Gucci book, she was later completely excluded from The House of Gucci film, which adapted Forden's 2000 book on the history of the family.

(My source for McLaughlin Loud's post-publication testimony is the article "SECOND ACTS; A Dark Gucci's Sunshine" by Ruth La Ferla for The New York Times, which was published on October 1, 2000, the same year that Sara Gay Forden's The House of Gucci book was first published.)

Based on Forden's own testimony in the book, as well as my own research into the Gucci family - including In the Name of Gucci: A Memoir by Patricia Gucci, the current Gucci family spokesperson, and daughter of the late Aldo Gucci* - it is almost impossible to verify precise historical accuracy when it comes to many claims from the Gucci family. For example, in The House of Gucci book, Forden spends some time sharing testimony from the late Grimalda Gucci (1903 - 1989), who contested several of the claims made by - and about - Aldo Gucci.

For a bit of background, Grimalda Gucci was one of the several children born to Guccio Gucci - the patriarch of the modern Gucci family, and the founder of the Gucci company - and Aida Calvelli Gucci, Guccio's wife. Grimalda was the sister to Aldo Gucci, as well as Rodolfo Gucci, who were played by Al Pacino and Jeremy Irons, respectively, in The House of Gucci film adaptation.

Grimalda, as the only daughter born to Guccio Gucci and his wife, and being surrounded by brothers, claims in The House of Gucci book that she was essentially shut out of the family business due to being a woman, while her brothers - specifically, Aldo and Rodolfo, though there was also a third surviving brother not mentioned in the film, Vasco Gucci - were groomed by Guccio, their father, as his heirs. Grimalda, who wanted a stake in the company, also claimed that she was also expelled from her board position as a family member by Guccio Gucci in favor of her brothers - Aldo, Rodolfo, and Vasco - despite having married a Gucci company executive, Giovanni Vitali, in 1926.

In turn, as seen in both The House of Gucci book and its movie adaptation, shares in the Gucci company - and executive positions - thus passed through the Gucci male line, as Aldo and Rodolfo groomed their own sons - for Aldo Gucci, Giorgio, Paolo, and Roberto; and for Rodolfo Gucci, Maurizio - to take over the company in their stead once they started to reach retirement age. However, Grimalda, who had no sons - or children - of her own, still contested being shut out of the Gucci company, decades later, and claimed that she had been shut out due to the sexism and misogyny expressed by Guccio Gucci; and, in turn, her three brothers, Aldo, Rodolfo, and Vasco.

Aside from taking a deeper dive in the sexism, misogyny, and patriarchy involved in conservative and traditional Italian culture - as I am not qualified to make that analysis - and regardless of whether or not Grimalda Gucci is correct in her claims, she also claimed that Aldo Gucci was not honest in his business claims and dealings. In The House of Gucci book, for example, Grimalda Gucci claims that Aldo "completely fabricated" the story that "the Guccis started as leather- and saddle-makers" before creating luxury leather goods, and that "Aldo had created the story as a means by which to market the Gucci company as more 'upper-class' and 'posh'", to paraphrase.

Grimalda Gucci's claim, in turn, is also indirectly referenced in The House of Gucci film, specifically in the scene where Aldo Gucci recounts "how the Guccis started as leather- and saddle-makers" to Patrizia Gucci, nee Reggiani, who had married his nephew, Maurizio Gucci. While Grimalda Gucci does not appear in the film, it is also clear that Grimalda Gucci's claims of being shut out of the Gucci company due to "being a woman" (i.e. sexism and misogyny) were adapted into Patrizia Reggiani Gucci's character arc in the film; specifically, with Patrizia Reggiani Gucci dealing with sexism and misogyny from her own husband, Maurizio Gucci - as well as Rodolfo Gucci, Maurizio's father, and one of Guccio Gucci's heirs - in seeking more power in the Gucci company.

Patrizia Reggiani Gucci, however, due to being barred from the Gucci company due to her gender in the film adaptation, ultimately crafts her husband, Maurizio Gucci, to be her tool, or puppet, in her attempt to circumvent the sexism and misogyny displayed by the Gucci family in the film.

Due to this, as well as Grimalda Gucci's claims that Aldo Gucci, indeed fabricated the story - if not other elements - of the Gucci brand, company, and public image, I would say that, while it is entirely possible that Aldo Gucci may have sold "fake Gucci products" on the black market, due to The House of Gucci book relying heavily - and solely - on Grimalda Gucci's testimony, it is impossible to verify if Aldo, indeed, did this. However, the book itself also notes that there is certainly evidence that Grimalda's claim that Aldo lied about the family's and company's origins, is, indeed, true; or, specifically, according to the book, Guccio Gucci worked as a lowly attendant in the Savoy Hotel of London, England, which is also referenced by Maurizio Gucci (Adam Driver) in the film.

As for a "fair depiction of the Gucci company in the 1980s", it is certainly in-line with what The House of Gucci book, as well as other books and third-party news sources and testimonials, claim. According to the book - and which the film also incorporated in its film adaptation of it - the Gucci company was in a period of steady decline from the 1980s into the 1990s, culminating in the last Gucci shareholder in the company, Maurizio Gucci, selling Gucci to Investcorp in 1993.

However, this decline was not solely due to the company potentially selling counterfeit Gucci products on the black market; a myriad of factors - including family infighting among Guccio Gucci's sons and grandsons as to the financial and creative direction of the company; company mismanagement; increasing competition from other, newer luxury good and designer fashion brands; and a decline in the overall quality of the brand's products due to cost-cutting measures, among other potential factors not mentioned here, all contributed to the Gucci company's decline.

Today, verifying information - or historical accuracy in regards to claims - about the Gucci family as a whole is difficult; not only due to potentially fabricated stories by Aldo Gucci, as well as a conflicting interest from Grimalda Gucci as a source, but also because the Gucci family has purposefully kept much information about their family under wraps to preserve their privacy. This is indicated by the Gucci family members declining to be interviewed by author Sara Gay Forden for The House of Gucci book, with Forden relying on found testimony from Grimalda Gucci for portions of the book in an attempt to reconstruct the Gucci family's obfuscated, murky past and history.

* - Answer updated to correct Patricia Gucci as Aldo Gucci's daughter, not his niece. Not addressed is Patricia Gucci's potential conflict of interest in portraying her father, Aldo Gucci, as "honest", as addressed in her autobiography, "In the Name of Gucci: A Memoir" (2016). I cannot address this due to r/AskHistorians' <20 year rule, including her words on "The House of Gucci" film, which are more recent.