Successful video games are all about telling an engaging story in an engaging way. If you take away the interesting elements of the story, you're pretty much left with gameplay to do all the heavy lifting.
In theory, I guess it's possible. The Sims does get kind of get close to this, but like Uchu said, it's not exactly representative of real life.
I think if we took The Sims, set it up so that you can only control one person, create some gameplay elements around progressing through school, work and life instead of just point-and-click stuff like The Sims (e.g. those minigames in Bully whenever you went to class)... it could work.