Yes, you can beat Fallout: New Vegas without killing anyone
You can safely add Fallout: New Vegas to the list of open-world titles which completely endorse the doctrine of complete and total pacifism. NeoGAF user Water_Wendi recently posted a screenshot featuring some braggable statistics after completing the game's campaign and nearly all of its quests: zero people or creatures were killed during the proceedings.
Well done, Water_Wendi! We can't imagine how hard it must have been to suppress the gamer's natural instinct to constantly murder. Now that you've completed this challenge, why not move onto one of these equally arduous goals?
Beat the game without talking to anyone
Beat the game without picking up any items at all
Beat the game without moving
Beat the game without encountering any bugs, glitches or crashes