^ Doubtful. Why would they delve into old Trek? They have already made their intentions clear when it comes to their focus on the new universe, not the prime.
New Trek kind of is
old Trek, after a fashion. If it's a story that's ready-made and unknown by the fans, there's no reason it couldn't at least be looked at and adapted as a potential treatment. If either of the rumors about Cumberbatch being Khan or Gary Mitchel are true, that seems like Abrams doesn't have much of a problem delving into old Trek at all.
The only in-universe thing that I would surmise keeping him from doing it is Vulcan's destruction in the previous film. Any moons in orbit, hidden weapon platforms or otherwise, would have been sucked in by the red matter singularity or thrown out into deep space, never to be seen again.