For the time being, I think onscreen Trek will exclusively be the adventures of Chris Pine etc in the JJ-verse.
When that comes to an end, TPTB will have to decide if they want to re-re-boot the series, they way Sony are doing with Spider-man or the way Chris Nolan did with Batman - ie new, even younger actors playing Kirk, Spock etc. This seems most likely to me - they are the iconic characters of Trek and once they're re-cast once, it can happen again.
You're talking about two different "they"s - Paramount for movies, CBS for TV. It's easy to see why a Star Trek
movie series would be attractive to Paramount - big-budget action adventure is the sort of thing they do.
Not quite so easy to make the connection with CBS. Where would they put a Star Trek
series? Not on CBS. Probably not on the CW. Showtime would probably prefer original sci fi ideas that aren't tainted by association with free TV. It just isn't an easy fit for CBS's business, compared with all the other shows they could be doing instead.
Whether CBS wants to do Star Trek
at all is a far bigger question than whether they'd want to re-re-boot TOS. It all depends on where the series would air.
Let's say CBS is going to sell the series to The Cartoon Network. That makes it animated, and then it becomes easy to see why it should be based on TOS - biggest name recognition, don't need to pay the Abrams movie actors to do the voice work, which can be done by other actors. But what's the advantage of a re-re-boot, vs just staying with Abrams' timeline?
Or let's say Showtime is going to air the series. In that case, they might want to avoid associations with previous free-TV series, because their business is all about selling shows at a premium that people could never see on broadcast TV. So that might mean the best approach is to make no reference to any previous series, including TOS, and reinvent Star Trek
in some striking and unique way.
It's probably best not to contemplate what the CW would do with Star Trek
Of all the likely possibilities, I don't see where a re-re-boot of TOS would be the most obviously successful approach.