Yes. There wasn't an American embassy in Venice, but during the Revolutionary War diplomatic agents of the continental congress did communicate with the Venetian Government through the Venetian Ambassador in Paris Daniele Dolfin. Although the Republic did not take sides in the Revolution, anecdotal evidence points to the fact that personal interactions between Dolfin and Benjamin Franklin were friendly.

There is a letter present in the Venetian Archives (which I can't find a higher quality image of) addressed to Daniele Dolfin signed by John Adams, Benjamin Franklin, and Thomas Jefferson in which the Americans attempted to open negotiations for a commercial treaty. Dolfin forwarded the letter in his dispatches, but Foreign Policy Committee of the Senate (the Savi dei Pregadi) chose to not bring the matter before the legislature.