The timeline has been altered/reset in such a profound way that the familiar characters from TNG should not even exist 80-100 years later after the time of new Kirk. Granting a generous exception to how new Kirk and crew still formed the Enterprise crew (again!) in the new timeline, any writer who gives life to Picard and familiar crew within the Abramsverse in the 24th century has clearly not thought this through. The human populace will turn out to be very different in the 24th century than what originally existed in the Prime universe.
That didn't stop every alternate universe story.
Also, based on Enterprise, Data ought to still exist regardless.
I think if they did have TNG characters show up in the Abrams-verse it'd more or less be the Picard-Data-Worf show.
Which, given the way they established Klingons in Into Darkness as the merciless killers referred to in DS9 Klingon lore, might actually be pretty awesome.
I don't think Picard's personality necessarily keeps him from being interesting to new audiences. His cerebral 'think it out' tendencies can be played against the more impulsive tendencies, only in the context of somebody Kirk does not have authority over and has to work together with as equals. Also Picard used to be more like Kirk, so he would be naturally annoyed at somebody who has all the personality characteristics he sees in his former self he's not proud of.
A young Picard/Data/Worf coming back in time might make a damn good movie.