In answer to the thread title, I'd say the likelihood of the current film series continuing beyond the next installment is largely dependent on two things: The success or failure of #3, and the availability of key members of the cast.
By most accounts I've heard, it sounds like Paramount has significantly
upped their expectations for the next film. If it fails to meet those expectations, I can well imagine the whole franchise might be sent back to the shop for retooling, a.k.a. the end of the "Abramsverse." New creative team, new cast, and probably a full reboot. Alternatively, they may just end it for the foreseeable future, but I think the former is more likely.
If it
does meet or exceed expectations then I’m sure they’ll want it to continue, but that’s when cast availability becomes a factor. As far as I know, all of the key actors were contracted for three films. Some of them like Pine and Saldana are in fairly high demand for other roles and will surely be expensive to bring back. Others may simply want to move on. I don’t think any of them, including Pine and Quinto, are totally irreplaceable in this day and age, but at some point it’s either not worth another film to do so, or the question of whether or not it’s the same “universe” becomes academic.
To address a totally separate topic, the debate over whether or not the Prime universe can or should be considered OUR universe as opposed to the Abramsverse or other alternate timelines, I have my own somewhat radical take on that. As a purely intellectual exercise, my own personal theory is that the Abramsverse IS our universe.
Think about it. What evidence is there in the Abramsverse that the Eugenics Wars happened in the 1990s, or at all? Obviously Khan still existed, was a product of genetic engineering, escaped Earth along with his fellow supermen and so forth, but he bears no resemblance to the Khan we all know from the Prime timeline, and he
should if the change didn’t happen until two and half centuries after he set sail on the
Botany Bay. I confess I haven’t rewatched STiD enough times to remember every detail but I don’t think the Eugenics Wars or any other specifics about Khan’s origins were ever mentioned.
What if he literally wasn’t the same person? What if the true point of divergence in the timeline was sometime prior to the 1990s and the Eugenics Wars were either long delayed or totally averted as a result? I could really go into detail and propose a scenario where Gary Seven, thanks to his encounter with future Kirk and Spock from the Prime universe, went on to influence world events so dramatically that he actually altered the foundations of the Prime timeline by preventing the Eugenics Wars and the 21st century Third World War from ever happening. In effect, he created OUR universe, which eventually becomes the Abramsverse.
Khan, or a version of Khan, still came along at a later date, perhaps even caused some significant trouble along the lines of the original Eugenics Wars before being driven off the planet. But instead of being almost totally forgotten in the chaos of the Prime universe’s 20th and 21st century world conflicts, enough records still existed for Admiral Marcus to actively track him down instead of waiting for the
Enterprise or some other ship to just stumble across him.
Many people have noted how different and much more advanced the technology appears in the Abramsverse, which could be explained by civilization not having bombed itself into near-oblivion a couple of centuries earlier and having to reclaim all of that lost progress. Building a starship on the ground in Iowa at twice the original size is suddenly not so far-fetched, to say nothing of things like ultra-fast warp speeds and interstellar beaming. Two or three hundred years worth of uninterrupted scientific progress could cover a multitude of continuity issues going much further back than the day of Kirk’s birth.
All of which is not to say that the Abramsverse is in any way conclusively OUR universe (as if any such conflation of fiction and reality were possible), but it at least has the advantage of not having overtly contradicted our own history with any on-screen dialogue, references or exposition that I’m aware of.
And lest anyone start hyperventilating over the prospect of the Abramsverse being the “real” Star Trek, or reading too much into my own preferences for one version of Trek over another, as I said, it’s merely an intellectual exercise.