A game would be possible, but it'd probably be a terrible game.
I actually doubt the mapping issue would be that bad. You could pretty easily come up with a clever way to turn satellite images or generic physical maps into at least passable maps for the game (buildings would be hard, but maybe possible if you used the shadows they cast to judge their dimensions). You don't need to create a world since it's already there and already digitized. Storing it would probably be dumb. Maps are already stored, so just procedurally generate the area when it's needed. Large-scale FPS gameplay is also pretty doable with modern internet connection speeds. Actually populating areas with NPCs would require some creativity, but would probably be possible (you could likely come up with a nice client-side way of doing it).
The issue is one of balance. The world isn't particularly well balanced. It's hard to imagine a way that Canada, for instance, could fight anything resembing a fair battle against the US. Moreover, there are strategic resources we don't use for a reason. If we want it to be realistic, people have nuclear capabilities. In real life, people don't just fire off nukes because it means killing potentially millions of people and potentially prompting a nuclear shoot-out that ends the world. In a video game, none of those concerns are really present. And there are no 13-year-olds with control over nuclear armaments in real life.
In fact, none of the conventions of war would need to be followed. What digital reason is there to avoid using biological weapons? Civilian casualties are essentially meaningless in a game, so that problem's gone too. Which brings up another issue of complexity. A lot of warfare is focused on cutting off supplies, so are you also going to simulate supply chains? Resource gathering? Weapon fabrication? It quickly becomes pretty infeasible and you're left with a basic, badly balanced, and ill-conceived game.
So yes, it's possible, it's just not a GOOD idea.
Edit: Also, given a map the size of the world, there's no reason the players would ever meet one another given even the most liberal estimates of playership.