If these guys were out there for the purpose of saving the Star League from destruction, then when Amaris took Terra they would have come a running for the fight. And after the fight they would have left in the Exodus, which would have gone to their world instead of to where it did.
The two main ideas, the secret world whose only job is to SAVE the Star League from destruction. And the idea of them going out there and cutting off all contact with home... are not compatible. The only way they could know the Star League needed saving is to STAY IN CONTACT with Terra. And since carrying out their mission requires them to keep in touch and know what is happening in the Hegemony... see the first paragraph.
And for them to know what happened and then NOT come running with all they had right THEN... they would have to betray their mission and turn against their purpose and no longer be any part of the Star League or have any yen to saving/rebuilding it. Hence they would have no reason to come back as an invasion fleet. And in terms of trade, over a voyage so far away it would be at least a year one way if not longer, they would not have much reason to do that either since they went out there with all they needed by way of manufacturing and industry to begin with.
Now, on the other hand. If these people were a bunch of Maine Lobstermen who wanted to go somewhere so far away their ancient Lobster culture could be saved from all the new age influences, and kids not going to church enough, and Lobster fishing being replaced landbased Lobster factory farms, and preserved intact. Well then, some rich Maine residents with influence might have put together a huge expedition to go waaaaay out there and build a Star League, fully self sufficient world, with the Maine Lobster colonists as their base population and established this world a hundred years before Stefan Amaris was born...
So they set out with their fleet, some RCTs, some factories, all the makings of a nice big Castle Brian, some good fire and brimstone preachers, plenty of fishing gear and a fleet of Lobster boats. Voyaging a few thousand light years out there, led by a member of the Cameron family, the first governor of New Maine, and built themselves a world and have grown and prospered and built factories, and farms, and lots of military equipment, and scientifically bred some truly fantastic Lobsters all these years.
Remember in Battletech, there is little of "American" cultures in the Inner Sphere, most of the "American" worlds were in the Terran Hegemony and got pretty much wiped out along with most of the people on them. A little piece of American culture waaay out there on its own all these years could be neat in the way that Comachos Cabolleros of the Southwestern worlds or the Trinity are neat.
So they left the Inner Sphere, went out, and built a new home and now forgotten by all save perhaps a small, well hidden underground anti-blake movement in Maine, who remember the expedition, and alll these years have waited and hoped and prayed for "The Return".
And so the Lobster Republic is back in town, sending a huge expedition force back along the ancient line of HPGs that once kept them in touch with their ancestral home. They knew the Star League died... But since putting together a fleet to come and fight would have taken at least a year, and the voyage at least a year, and since when Amaris took over he wiped up the HPG stations and it took a few years for them to even hear about what all had happened and they knew it was way too late for their division or two of troops to be able to save anything... they didn't come back.
They just moved on, and lived, and built, and grew stronger until the year came that a charismatic young fire and brimstone preacher or a Cameron descendant (Or Both) started up a movement to go back and kick somebody's butt and while they're at it, give those folks that still dwell in Maine a chance to get out of there and come live in the Lobster Republic.
And now here they are, big, bad, with Red Mechs and tanks and space fighters and warships painted Red and proudly showing the Claw, the symbol of the Lobster Republic. They don't think mcu of the Houses that looted and burned the Hegemony's corpse, no they don't. And them Clanners, that bunch is lower than a Louisiana crawfish. And the Word of Blake, who have banned all Lobster, crab, and shrimp fishing on Terra in the name of the "environment"... words don't describe how the warriors of New Maine and the Lobster Republic feel about those WOBs.
Beware the Claws of the Righteous.