I've deliberately lost my capital to watch my empire split. And it does split. The split will not be even, however. You will retain the more powerful faction.
If there are already 7 civs, and a capital falls, no split can occur.
Recently, the Chinese empire the Sten Sture's OCC reference game (4 whales) split when I was attempting to conquer the world as a OCC. I wiped out the defenders, and reduced the population to size one (in OCC, you can never, ever have more than one city). When I took the size 1 capital (destroying the city), the Chinese empire split into Chinese and Spanish "Rebels". The spanish were much weaker, and the two fought madly! I let them help me destroy each other. Since I only had one city, I was not viewed as a big threat, LOL... even with my stealth fighers from my carrier killing by the bushel... But the unexpected empire split was a great help to me in that game!