Short Answer: No.
Long Answer:
Naoki Yoshida feels that Final Fantasy XIV has a unique freedom and responsibility as a Final Fantasy Online title. On one hand, it has to continue on the tradition of each numbered title having its own cosmos and mythology. On the other, not only is this one of the only Final Fantasy mediums left whereby "player creates hero" is still a thing, but people will be playing it together. He seizes upon this by taking the nostalgia higher than moogles and chocobos, allowing it to be a celebration of every Final Fantasy, especially the early [Mysterious Warriors of Light] titles. In his own (paraphrased) words: "Final Fantasy XIV is meant to be an amusement park where every Final Fantasy inspires its own attractions."
Even when things bear the same names, even when they bear the same look, even when they have similarly blank histories, they are NOT the same thing. Final Fantasy XIV is isolated, and even familiar things are forks unique to Hydaelyn with their own histories and identities molded to fit this world. Some things simply undergo less modification than others, because just as there's a time to own your invocations and take them somewhere new and exciting, there's also a time and place for old friends to transcend their spritely forms and manifest in the glory of 3D with minimal liberties taken.
On occasion, there will be a pseudo-canon fun-time event that stretches these rules pretty much to the breaking point, but notice that they always blame the other game and are never mentioned outside of their own bubble. Nothing in Final Fantasy XIV allowed Shantotto to appear, Shantotto did it; she's that powerful in the world of Final Fantasy XI. Nothing in Final Fantasy XIV allowed Lightning to appear, Bhunivelze did it; he's that powerful in the world of Final Fantasy XIII. And, then, of course, Yo-Kai Watch, lol. Like Hildibrand, they're as canon as each individual wants them to be.Originally Posted by Kazutoyo Maehiro (Main Scenario Writer; 2.0, 3.0)
Soon, Return to Ivalice will be added. This one is the big one, imho. When it comes to DLC and bonus dungeons and re-make homages (other types of pseudo-canon fun-time), all bets are off. However, occasionally, one director can truly "opt-in" to another world. It's an iffy thing; modifying another team's creation and inserting yourself into it is ethically dubious, imho (at best). And I say that while acknowledging that Square Enix repeatedly kicks the hornets nest by creating things like Dissidia and Mobius, using the multiverse to justify the grouped nostalgia, knowing full well that some people will apply it in reverse and ignore the authority of a game's director when claiming that their creation is isolated.
However, with Return to Ivalice, you have Naoki Yoshida and Yasumi Matsuno, the creator of Ivalice himself, working together. Pretty much anything goes, and without question, when you have that level of blessing. We asked Yoshida if this finally burst the isolation bubble, and he said:
So something mysterious is up, but even this technically doesn't fully opt-in.Originally Posted by Naoki Yoshida
This was recently broached yet again in the big picture of the multiverse, when Omega appeared and created enemies from Final Fantasy V. Even though the game went pretty far out of its way to show that Omega was a creation "from a distant planet" that was host to "an advanced civilization" and that all of these creatures were from the fourteen prime dimensions (some based on fictional accounts, at that), it still needed to be stated outright that:
Over the years, people have assumed Final Fantasy XIV is actually, canonically, concretely, somehow to Final Fantasies III, V, VI, XI, XII, XIII, Dissidia, and Mobius. But they've rejected every opportunity to opt-in to anything more than cross-over gimmicks for the sake of fun and profit, and so the bulwark holds for now.Originally Posted by Naoki Yoshida
Zodiark of Final Fantasy XIV bears the name of a god of Ivalice, but the Dark Father is merely wearing some of his themes.