Contrary to what I hoped or expected when I posted the question, the picaresque novel didn't have much of an impact on Italian literature. Matthias Bauer's monograph Der Schelmenroman (Stuttgart: Metzler, 1994; "Schelmenroman" is the German term for picaresque novel) discusses Spanish, German, French and English examples of picaresque novels and authors who were influenced by it, but not a single example from Italy.
Harry Sieber's monograph The Picaresque (Routledge, 1977, reprinted in 2019) points out that
Translations of Spanish picaresque novels appeared in Italy slightly later than in other European countries. These translations, however, did not inspire the writing of what could be called an Italian picaresque novel.
That sounds like a definitive answer to my question. More interesting, perhaps, are the reasons why the picaresque novel has so little impact in Italy:
One [reason] is that Italy already had a strong history of the kind of novelle that Barezzi included in his translations. This native tradition contained tales of trickery and fraud similar to those found in the picaresque, many of which cam from the general store of facetiae or from other sources such as Theseus Pinus Urbinas' thirtheenth-century De cerretanorum origine eorumque fallaciis. Italy also had a long tradition of liber vagatorum literature. The blind beggar if the Lazarillo, Guzmán's fraternity of vagabonds in Rome, Pablos' partner, Valcazar, a false beggar in Madrid, and the hundred odd wandering students and thieves which populated the Spanish picaresque, were commonplace in existing Italian fiction.
The Picaresque: Tradition and Displacement, edited by Giancarlo Maiorino (University of Minnesota Press, 1996) agreed with Sieber's explanation:
Stories of trickery and fraud were common to Italian literature at least since Boccaccio, for instance, (…).
Nevertheless, some scholars have described a number of works of Italian literature as being more or less in the picaresque tradition. For example, Peter Brand's The Cambridge History of Italian Literature (Cambridge, 1996) mentions Francesco Fulvio Frugoni's Il cane di Diogene (1689),
in which the dog Saetta describes his life with his master, the philosopher Diogenes. It is a work in seven 'barks' hovering between picaresque novel and moral treatise, full of digressions and satirical thrusts against the world of courtiers and men of letters, combining both learned and popular elements.
(For what it's worth, the Italian Wikipedia article on Francesco Fulvio Frugoni describes Il cane di Diogene as a work of satire and does not use the word "picaresque".)
In Rewriting the Journey in Contemporary Italian Literature (University of Toronto Press, 2008), Cinzia Sartini Blum mentions (on page 144),
the 'spontaneous, robust, popular speech' of Teresa (...), the protagonist of Maraini's picaresque novel Memorie di una ladra (1972, trans. as Memoires of a Female Thief).
Johannes Hösle's Die italienische Literatur der Gegenwart. Van Cesare Pavese bis Dario Fo (C. H. Beck, 1983) devotes one third of a page to the feminist author Dacia Maraini without mentioning Memorie di una ladra or the picaresque novel.
Italienische Literaturgeschichte, edited by Volker Knapp (third edition, Metzler, 2007) doesn't discuss the picaresque novel or Francesco Fulvio Frugoni. Maraini's Memorie di una ladra is described as "letterature selvaggia" without explaining that term.
The entry for picareske roman in the Dutch Algemeen letterkundig lexicon categorises Memorie di una Ladra and several other twentieth-century novels as neopicaresque, which is not really what I had in mind when I posted my question.
Conclusion: Italian literature has not produced a novel that scholars agree upon to be entirely in the picaresque tradition.