Referencing Star Trek - The Voyage Home, where Kirk saves the whales by traveling back in time to San Francisco.
Are whales extinct in the Kelvin timeline? And did the "Probe" ever visit Earth?
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Fundamentally, we don't know, but humpback whales are probably extinct, at least during the events of the feature films we've seen so far.
There are two basic points of view. One is that everything that happened before Nero's incursion into the past is exactly the same in both timelines. Although I can't find good quotes from Orci that specifically state this, this seems to be the attitude the writing staff from the first movie had. They also have an attitude that even events AFTER the split are more-or-less the same (with some big differences of course) because (quoting from this interview):
We can do whatever we want. However, the rule that we have for ourselves is that it has to harmonize with canon. This is going to get way too geeky, and I apologize ahead of time… Quantum mechanics, which is how we based our time travel, is not just simple time travel. Leonard Nimoy didn’t just go back and change history (as Spock Prime in the 2009 film), and then everything is like Back to the Future. It’s using the rules of quantum mechanics, which means it’s an alternate universe where there is no going back. There is no fixing the timeline. There’s just another reality that is the latest and greatest of time travel that exist. So, on the one hand we’re free. On the other hand, these same rules of quantum mechanics tell us that the universes that exist, they exist because they are the most probable universe. (...) And, therefore, the things that happened in The Original Series didn’t just happen because they happened, they happened because it’s actually what’s most probably going to happen.
Under this view, humpback whales absolutely don't exist at any point in time that we see in the Kelvin timeline, and the probe might have visited Earth in the distant past (if it did when they first made contact with whales--this was never specified), and for the same reasons it did in the Prime timeline probably will appear a few decades after Star Trek: Beyond.
Simon Pegg, on the other hand, wrote this in a blog post about Sulu's sexuality (which may arguably have been altered in the Kelvin timeline despite being born before the point of divergence)
With the Kelvin timeline, we are not entirely beholden to existing canon, this is an alternate reality and, as such is full of new and alternate possibilities. “BUT WAIT!” I hear you brilliant and beautiful super Trekkies cry, “Canon tells us, Hikaru Sulu was born before the Kelvin incident, so how could his fundamental humanity be altered? Well, the explanation comes down to something very Star Treky; theoretical, quantum physics and the less than simple fact that time is not linear. Sure, we experience time as a contiguous series of cascading events but perception and reality aren’t always the same thing. Spock’s incursion from the Prime Universe created a multidimensional reality shift. The rift in space/time created an entirely new reality in all directions, top to bottom, from the Big Bang to the end of everything. As such this reality was, is and always will be subtly different from the Prime Universe. I don’t believe for one second that Gene Roddenberry wouldn’t have loved the idea of an alternate reality (Mirror, Mirror anyone?). This means, and this is absolutely key, the Kelvin universe can evolve and change in ways that don’t necessarily have to follow the Prime Universe at any point in history, before or after the events of Star Trek ‘09, it can mutate and subvert, it is a playground for the new and the progressive and I know in my heart, that Gene Roddenberry would be proud of us for keeping his ideals alive. Infinite diversity in infinite combinations, this was his dream, that is our dream, it should be everybody’s.
Under this view, anything goes (but with the understanding that a lot of things are still pretty dang similar in both).
So, theoretically, it's possible that in the Kelvin timeline, humpback whales still exist without time travel reasoning being involved. As far as I know, we've seen no evidence for it, and considering how many other things tended to stay the same, despite wild changes, Orci's view has some weight behind it in regards to most of the past. Probably, Humpback whales went extinct on schedule in the past of both timelines. Probably, the probe still visited in Earth's distant past (if that is indeed what happened in the Prime universe).
Now, because of time travel, we here get into a sticky and thus-far unrevealed part of canon: Did, in the Kelvin timeline, the crew of the Enterprise (albeit using a Klingon Bird of Prey) appear in the 80s to steal two humpback whales and bring them to the future?
Again, we don't know, we haven't reached the point in the Kelvin timeline in which they would have made that trip, nor do we know whether previous temporal incursions 'stick' despite the timeline changing (this might in fact be related to Pegg's outlook, the entire history of the universe might have subtly changed in part because of all the time travel that people from the Kelvin timeline would eventually have done differently, or not done at all, that made small alterations to the pre-Kelvin history as well).
So it's possible that, as in Orci's view, the most probable course of quantum events is, in a couple decades, the probe returning and devastating Earth while it waits for a reply, Spock (but now Kelvin-Spock) still figuring out they need Humpback whales, and using the time travel trick to go back in time to get them, and return.
Or it's possible that this will have been changed too, maybe the Enterprise crew is in another part of the galaxy when the probe returns (after all, Wrath of Khan must happen much differently, or not at all, after Into Darkness, and the ship's status and mission in III and IV all spiral directly out of events in II), nobody else will think of going back in time to get whales, nobody ever appeared back in the 80s either, whales are still extinct, and Earth in the Kelvin timeline is in severe danger when it reaches the equivalent time period of Star Trek IV.
Or, it's possible that a Klingon Bird of Prey (piloted by the Prime-Crew) appeared in the 80s to kidnap whales (and the disappearance of said whales, the scientist studying them, and any other associated historical impact from STIV is recorded by the Kelvin timeline's history), and yet again no corresponding Klingon Bird of Prey goes back in time to get them and returns to put them in the ocean (because they came from, and returned to, the Prime timeline) and whales are still extinct so Earth is likely doomed in this scenario too. (But we'll probably never get to see how that winds up affecting the future of the Kelvin timeline and maybe they'll find another solution...)
Or it's possible (though unlikely) that in the Kelvin timeline whales aren't extinct BECAUSE George and Gracie aren't removed from the population in the 80s, and that made all the difference, so there's no reason for the probe to revisit.
That's a lot of possibilities, as must be expected when you're dealing with an unrevealed part of canon complicated by something like time travel that hasn't been used with consistency over a show's run, but most of the possibilities still point towards humpback whales being extinct at least during the timeline of the movies.
It should be noted that ST:IV mentions Humpback Whales, not all known species of these marine mammals.
According to Memory Alpha, Humpback Whales were extinct during the 21st century due to overhunting. So it is safe to assume, even if the new movies never mention these events, that they are extinct even in the Kelvin timeline.
About the Whale Probe, it is of unknown origin, so we can't say if the events that lead to the creation of the new timeline affected it in any way; we don't know if its destiny was somehow changed.