I think that the key determinate between the unlikly that happens (Bonaparte becoming Napoleon I, Ghengis Khan, the Rise of Rome) is that while they were quite wildly successful, there's nothing unusual about their acts in the time they were happening. Rome is a town on the Tiber... with uncommon skills at utilizing every bit of available manpower and presenting a united front to outsiders, at least compared to its neighbors. It's easy to see how that snowballs into an Empire. Bonaparte is a talented man with specialist training, facing an army that has suddenly had command opened to the talents, and was desperate for specialists - talent and training means he will rise. The Mongols were very good at step-nomadism : and a talented leader willing to fold other tribes in could, and did, go far with it.
Many early-Medieval-Caliphate-as-Borg scenarios require groups of Berber and Arabian tribes to act with the motivations of Front National scare pamphlet. These motives and drives would have been alien to them: mostly, they were looking for better land, plunder, and the chance to find a place to set themselves up on top. They don't have the time machine to realize what they really want is Eurarabia, and the oppression of redditors yet unborn. When they've carved out their niche in a more hospitable area, they'll stop.
In the Civil war scenario, Lord Palmerston wants a thriving British Empire (that's hopefully quieter than 1857-1858....). He needs to protect Britian's freedom of navigation. He'll do a lot for that. A whole lot. He does not have an inkling of the eternal Pax Britannica certain to happen (if it's that certain) if the United States is cut in two. Nor does he have an altruistic desire to start a lengthy and expensive war that will compromise British interests and prosperity for the sake of a Lost Cause that will not exist until the 1880s. He is stuck with the motivations he has in his time, which can cause a plausible war. But the scenarios for many of these wars that don't draw on the existing motivations are risible, as are the ones that turn real and profound advantages Britain had into super powers.
The difference between the Borg Caliphite and Lost Cause scenarios and the actual rises of Temjin, Bonaparte, and Rome is that the ones that happened all flowed from things in their social and political environment. ATL's flowing from a similar sources seem highly believable. Ones that require the parties to be play actors in the political dramas of centuries or millennia hence are less so.
