In theory the answer is yes; in practice, the reality was a bit more nuanced. Although there certainly was a fervent intellectual camp in favor of Classical Latin as the Miglior Lingua, or "Better Language," and Latin continued to be used for things like scientific books and some legal affairs (albeit in a steadily declining proportion) Latin-bashing was a favorite pastime for a number of intellectuals, including Dante Alighieri. Although the study of Latin was part of all classical curricula, people had stopped actually speaking Latin as a first language long before the 16h century.

In the specific case of Venetian, there are countless examples of the vernacular used in print: the Flors Duellatorium is a fencing manual very clearly written by a northeastern vernacular speaker, while the Republic's treaties with other Italian states are peppered with venetian-isms, and for years english-speaking scholars couldn't find much information on England's first explorer, Giovanni Caboto, because documents in his native Venice written in Venetian even had his name down as the local variant Zani.

However, by and large the very active Venetian literary scene was dominated by intellectuals who were well-versed in medieval Tuscan poetry, and made a point of showing it. In fact, although many texts might betray their author's origin by inserting venetian-isms here and there, by and large Venetian publishers and intellectuals were some of the strongest lobbyists in favor of the adoption of a unified Tuscan-based Italian language: in 1516 the northeastern writer Giovanni Francesco Fortunio published Regole, a formalized grammar book based on 14th century Tuscan literature, while in 1525 the cardinal and humanist Pietro Bembo, also a Venetian, published a very successful book titled Prose della Vulgar Lingua arguing in favor of writing in the style of the literary Tuscan of the 14th century.

Venetian publishers and intellectuals' enthusiasm even baffled some Tuscans, and Niccolò Machiavelli himself wrote a brief book titled "Defense of the Florentine Language," where he explains to a Venetian straw-man, named Messer Maffio, how illogical it is for a Venetian to pontificate about Tuscan grammar, as it would be for a Tuscan to write about Venetian grammar. But book publishers were (and still are) interested in making sure that their books are as widely sold as possible; and although the Tuscans got defensive about it, writing in an approximation of their language was the best way to make a book widely understood. Writers in Venice, and indeed the rest of Italy, were also interested in making their works as widely distributable as possible, so there was little need for discussion with their publishers to agree that imitating Tuscan was the best route to this effect.

The only real opposition came from a curious intellectual current lobbying in favor of a sort of pan-Italian pidgin: it would seem that a sort of unwritten "Courtly Language" had developed as the elites of the Italian states grew closer through marriage, diplomacy, and trade. We unfortunately have close to no idea as to what this language might have looked or sounded like; the keystone work by its leading sponsor Vincenzo Calmeta has been lost to time, leading some to call it a "Ghost Language." Research in the '90s (Drusi 1995 and Giovanardi 1998) postulates that the "Courtly Language" was an unstructured form of vulgate modeled on the language of the Papal Court in Rome, which accepted a high number of Tuscan-isms, but was not derivative of it. I however, have always interpreted it as having a Lombard base, seeing as its two greatest sponsors, Calameta and Castiglione, were from Lombardy; however it's also important to point out that the people speaking the language would have all been tutored in the same classic Tuscan literature, meaning that the overall Tuscan influence must have been undeniable. Castiglione, who gives no description of the language, in his writing argues that language is a purely functional tool; and as such favored a completely unstructured form that could even vary from court to court, as long it was intelligible.

But the whole point of formalized grammar is to make sure that everyone's using the same words, style, and structure, precisely so that everyone can understand each other. Book publishers, which were highly concentrated in Venice, were already publishing a tons of books of Tuscan poetry, and the people reading and writing new books were all tutored in that poetry; so it would seem that Tuscan was just too convenient a choice. Although it's often easy to discern where a renaissance author grew up based on their vernacular quirks that seep into their writing, very few authors made a point of writing exclusively in their own vernacular. Even Carlo Goldoni, the great Venetian playwright, has his well-to-do protagonists speak in "proper Italian" while working-class characters speak in Venetian. Goldoini did write some works entirely in the local dialects of Venice and the lagoon, but only as a kind of pet side project.

So much like ordinary people in modern Italy, a Venetian intellectual would moderate his speech based on the situation. Especially when publishing a book, by and large a more understandable language would be preferred. A more refined language would also be expected in high society. Emulating Dante while buying groceries, however, would be pompous.