Here's something to think about and to arouse nerds.
Disney has partnered with Paramount for the Avengers flicks and has a good working relationship with them. Now that Disney owns Star Wars and Paramount still owns Star Trek, it's conceivable the two worlds could somehow connect. (Such as E.T. being in The Phantom Menace)
The worst part is that the movies won't have the 20th Century Fox fanfare at the beginning.
Plus, Star Trek takes place in the future. Star Wars takes place a long, long time ago in a galaxy right down the street from Jay Leno's face.
*I apologize for that seemingly random reference to Jay Leno's "Is His Head Bigger Than Mine" sketch*
I doubt they would have plot lines interact, the two are too different. But I wouldn't be surprised to see a Klingon in a Cantina or a Feringi flying a spaceship.
Again, they've already done this with E.T.