I would speculate that Spock would keep an eye on how events unfold in this new history and if he did intervene it would be for really serious problems that may crop up because of how things have been changed.
The idea of smoothing the way to allow for a completely different set of adventures has its appeal, I admit.
On the other hand, there is no denying the draw of reimagining how a classic story might be retold. For example, I would not have Khan picked up, match wits with Kirk for a while before trying to hijack the Enterprise. Instead, I would show him actually accomplishing one of his long term goals of building a new Empire for himself. In the new version of history, wouldn't it be interesting to see him as the figurehead of a new political force or ideological movement, with ships and a planet (or planets) answering to him, and the Federation having to play a dangerous political game with him?
I also have to give a nod to those who have pointed out that Spock has faith that the universe will unfold the way it's supposed to, even if that includes a disaster; you do the best with what you've got, earnestly. So, not too much cheating, if any. Notice that he didn't explore too deeply the circumstances regarding the Enterprise crew roster, and wasn't a stickler for adhering to specific Stardates. He finds out that Kirk and his younger selves roles are reversed. We don't even see him informed of important contextual details: Kirk is a cadet who is maybe close to graduating, yet he has been fortuitously place in the chain of command. We can see though by his interference that he is convinced that Kirk needs to replace his younger self as captain of a starship called Enterprise (he doesn't know the capabilities of the ship, how different it might be). Even if Kirk takes over, he has know way of knowing if his younger self will pull himself together and work with Kirk in the way he obviously hopes will happen. He really does have faith that the Enterprise under the command of James Kirk will make sure that what needs to happen with Nero will happen. He does cheat, though, because without it Kirk would have been eaten, and the Earth would likely have been destroyed while Enterprise tried to coordinate with the fleet. I wonder how he will react when he realizes that he's helped Kirk become captain of the Enterprise 6 to 8 years before he did in the original version of history.
One final thing in this rambling post, insofar as what I think Spock will be up to. Spock is, among other things, a scientist. At the very least, he can track the development of this new history, and compile a side-by-side comparison with the history he remembers. I imagine this would be a private, ongoing project. From a scientific standpoint, the "Prime" universe can be regarded as a control, and the new history as a "test" or "experimental" history. The side-by-side comparison is scientific data, from which one could formulate theories; and Spock could very well pioneer new thinking about time and time travel theories. Exactly when to make the data available for release safely is something of an ethical concern, but he might be reasonably safe with having it open for public scrutiny around the corresponding year that he and Nero would have left The Next Generation timeframe.
His observations of how the two histories differ might give supporting evidence for the Butterfly Effect, the elasticity of history's "shape", and if there seems to be a corrective momentum in the way history unfolds.
I figure Spock will have much of interest to keep himself occupied, aside from efforts to help rebuild Vulcan society and culture, and dealing with how his presence and identity complicates his place in the new history.
), now that Vulcan has gone so if Vger comes into play how will be played out? 
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I doubt there would be wide spread panic.
