A hypothetical for you guys:

Just say that Caesar's Legion didn't push their army west, but instead went east. They cut through the Midwest Brotherhood of Steel like butter (or maybe they went the same route as Lyon's BoS, finding nothing but tribals and petty raider gangs), and eventually find themselves standing http://images.wikia.com/fallout/images/f/f0/WelcometothePitt.JPG.

Let's assume that the Legion doesn't cross the bridge into The Pitt guns blazing, but instead Caesar sends his Frumentarii into town, where they meet with Ishmael Ashur.

What happens next?

The Legion Cutting through the Midwestern Brotherhood like butter? Not going to happen.

If they took the same path as Lyons or somehow found their way to the Pitt. They would simply take it over like every other place. They would promise Ashur anything, and Ashur would fall for it. When the Legion finally makes it to the Pitt in full force.. They would kill every person in it, for being mutants.

If Ashur finds the cure for people to stop becoming Trogs, then the Legion might go in a just enslave everyone and have their own people take over the factories.

If Vegas is taken and they expand eastwards with Caesar at the helm...well here's how the battle will play out.

Frumentarri will befriend Ashur. They'll act as independent agents and mercenaries who will spy on the rebels and feed him false information about the rebellion. Using Ashur's raiders, the Frumentarri can easily disguise as rebel slaves and get information. Using that information, they'll lead Ashur's largest army into the biggest fight of their life.

While both sides are weakened, the Centurions and the Legionaries will attack both weakened armies and clean up after that. Simple, swift, and considering we're dealing with tribals on both sides, bound to work.