There was a time when it probably could, like Fountain or Guernica or Raft of the Medusa or David or the Sistine Chapel ceiling or photos from Vietnam or the moon or whatever. But we've evolved past that. Long past that. Postmodernists probably feared changing the world, and we've probably moved past them too (though they're still out there, lurking in the shadows).
Art still has meaning in it, but art only touches people on personal levels these days. There's no overwhelming consensus on Joseph Kosuth or Kiki Smith* or Banksy. A Family of Man-style exhibit could go over well in certain contexts (provided there were enough famous photographs in the show to draw big enough crowds), but overall responses would sound more like "Wait, that's supposed to be me? That's not me!" than "Oh my gosh! We're, like, all the same! Hugs!"
Famous works of art have an easier time changing art nowadays than changing the world. And even changing art is a difficult task, considering art changes all the time or not at all, depending on who you ask.
There's too much individualism in movements and actual works for any singular person or piece to change the world.
That's not a bad thing. Not in the least. The bad thing is the people who are kidding themselves by thinking that their work - or anyone's work - is going to change the entire world.
* Kiki Smith is German. Did you know that? I did not.
