If by "public" you mean other bishops, priests, monastics and laity, then you would be right.
Indeed, and unlike in the Roman Catholic church, where a Pope can uniltaterally making a sweeping and unpopular decision like Traditiones Custodes, in the Orthodox Church no single bishop has that much power, and to the extent synods and councils do have power, the laity can reject them. This is why for example the Arian synods like the Council of Antioch have no canonical status despite being theoretically valid assemblies of bishops in apostolic succession.
Now I do pray for eventual unity between Rome and the Orthodox respecting the autocephaly Orthodox bishops enjoy under Canons 6 and 7 of Nicaea, however, had Florence been adopted in the fifteenth century, during the Avignon Papacy, the Borgias, etc, everything Catholics love about the Orthodox church today including the mystical theology, the monasticism, Hesychasm, the liturgies, the iconostasis, the Octoechos, Palamist theology, etc, would have likely been lost due to Latinization, and while we might have kept Constantinople as a Christian city, visiting it would be a bit like visiting Ravenna, with predominantly Latin services in Byzantine churches. It is also possible such a union would have done nothing to prevent the Protestant Reformation and indeed, if aggressive Latinization happened in the Byzantine Empire, it could have spread to it due to people being annoyed with non-vernacular liturgies and communion in one kind, as it happened in that selfsame century in Moravia, where the formerly Orthodox people led by St. Jan Hus (venerated as a martyr in the Orthodox Church of the Czech Lands and Slovakia) rose up to reclaim what they had previously had before the Hapsburgs conquered Prague and the surrounding environs and everything was Latinized.