No, there is no component of Virtual Villagers left running when you exit the game. The game doesn't check Internet time, either. What does happen is that the game performs calculations based upon the current system clock setting when the game is launched, and the system clock setting at the time the game was last exited. The game cannot possibly determine whether or not the clock is "accurate" but it can, and will, become unpredictable if it ever encounters a "backwards" movement in time.