I don't think so. And you also have to remember that the empire (actually it was a Triple Alliance that subjugated other states into tributaries under their hegemony) was only formed in 1428, and they didn't even expand to the coasts until the reign of Moctezuma I, in the mid-1400's. Meanwhile Cuba is quite far away even from the coast of Yucatan, at least as far as canoes go. Mesoamerican canoes could be quite large and the Maya and related groups were good sailors and experienced, but even they didn't go to Cuba. The Aztecs however are way far away, on the complete opposite side of the Gulf of Mexico. I'm not an expert on sailing and navigation, but it might be feasible to have some Mesoamericans go there with the right POD, but they wouldn't be the Aztecs.