Oh, there would certainly be a last ditch holdout in Bretonia. But there's a serious problem.
By the time you finish Mission 13, Rheinland has full control of at least the Honshu system and is close to conquering the New Tokyo system, Liberty is under complete Nomad control and invading Shikoku, the Kusari Navy has been almost completely wiped out (along with a significant portion of the Blood Dragons), and criminals in Liberty and Rheinland have been beaten back enough to be unable to influence them for a fair amount of time. Rheinland is also either just about ready to launch a full-scale invasion of Bretonia or already has, keeping the BAF occupied.
There's no force in Sirius that could stop them. The Order had some really good pilots, but Edison Trent could only be in so many places. He could not, by himself, fight off the greatly enlarged Liberty and Rheinland navies at the same time (not to mention the Nomad fleet, which while not as large as a House Navy is still quite significant). Kusari had already fallen by the time you entered the Dyson sphere, if the Nomad fleets were still there they would be in the process of cleaning up rather than conquering- things like infesting the Shogun, wiping out pirate factions, etc.
If Edison Trent had failed, the Order would have been slaughtered to a man. Even as it was, Toledo was leveled and they lost a lot of people. But if they hadn't opened the hypergate...
Bretonia would probably have only a week or so before receiving the full onslaught of the Nomad forces. Remembering that SP takes place across eight months or so... that isn't a lot of time. Bretonia, however gallant and incorruptible, could not hope to stand against the titanic navies of Rheinland and Liberty, as well as any Nomad ships remaining from the slaughter of the Order. Shortly thereafter, Malta and Crete would be overrun. With the major factions out of the way, deposed, or on the run, the steadily growing Nomad forces would infest or eradicate every last bastion of humanity. Hidden pirate bases could not stay hidden if an entire Navy went into a cloud looking for them- there would be no place to hide, and ships can only run for so long.
Edison Trent did not stop humanity from taking major losses. Humanity was a hair's width away from complete and utter annihilation. That's not something to be taken lightly- think about that. It's often quite difficult to realize how lucky you are unless you think about what would have happened otherwise.
EDIT: In light of recent comments, of course they wouldn't go out without a fight. But even every pilot free of Nomad control during Mission 13 could not beat back the Nomads. Two hyper-inflated militaries, the Nomads' own ships, and three houses already under subjugation? Not to mention cloaking devices? Do you really think that a battleship at every jumpgate and jumphole into Bretonia (there weren't half as many left to do that, as it were) would be that much of a threat if the entire Rheinland Military jumped through and decloaked? Not to mention the amount of coordination that would require, considering how much the Nomads kept people in the dark about their goals? A pre-planned exodus might keep Bretonia safe for some time, but they couldn't hold out forever. If necessary, the Nomads could just lock them inside and build more ships- they had all of Sirius to plunder (not to mention what cardamine does for the Nomads) and Bretonia is close to being mined out.