That's similar to what I had planned. Missions would have a 'countdown', of a sorts, and if you didn't do anything, well, sometimes nothing happened, sometimes an NPC might die, etc. etc.
Of course, I'm not using dice, or a leveling system, equipment stats, etc (chalk it all up to ignorance eventhoughimgearinguptodelveintotheoldworldofdarknessettingandthissettingwouldbevaguelyinspiredbyit) The only real reward from these 'side quests' would be the enjoyment of writing!