i would prefer to think of it as just that timeline, but would love to imagine that there are plenty of ships going on plenty of adventures out there.
Into Darkness was (clumsily) trying to show that timeline sort of "righting the ship" when it comes to starfleet returning to an exploration culture following a few years of post 9/11-esque military paranoia, culminating in the whole khan/uss vengeance thing.
note: i really do like the story they are trying to tell there, it's about the dangers of losing your way in light of an aggressive catastrophe (in this case, the slaughter of the fleet against Nero in the first film), i just think they told it poorly.
aaaanyway, there's no reason why you can't have another ship and crew out there who are pushing the old line of exploration and trying to leave the dark years behind, could be a great thing if done right.