Honestly, this "could work" in therory. America didn't started off as a bunch of people "coming" together spontaneously. There were 13 orginal colonies which started to grow, more colonies joined and more "acquisitions" were made, etc. and the rest is history.
But in the case of Africa, as someone mentioed earlier, there are hundreds of different tribes. What will make any one of them want to join the next.
If anyone has read early social contract theories.....ie. The Republic by Plato--a great agruement is posed. People collectively give up some of their powers to join this "social contract" because its better for them overal. If provides protection and security for the "little people." But what about if I'm a big tribe and I think I'm doing pretty well, my people don't need protection. What incentive do I then have to join this contract? That's one of the fundamental problems of uniting people under one government.