The contemporary characters would be people who, in some way or another, will be important in the future. The characters would be up to the players to make them relevant - if they're not, I wouldn't accept them into game. As shapers of the future, the clones and the travelers would all have a stake in dealing with them (either to kill them, stop them or make sure they progress unimpeded).
The social networking aspect would end up being used as a tool by the two groups - it would be laughable if soldiers on a mission get bogged down in mundane relationships... although perhaps not impossible.
Would you be interested in becoming involved with this game? I'm asking because you have some very good ideas and I'm enjoying talking over the plot with you.