Well, whether it could happen or not, the world would quickly devolve into chaos, factions and groups fighting for ideological charges. Maybe not physically, but definitely terrible political, religious, and social struggles. Unforgiving, unrelenting... a veritable Hell on earth.
Think of about eighty or so Cold Wars going on at the same time. It may be that nothing would actually happen, but the tension and anxiety in such a would be able to be cut with a knife.