Ahh...I do think that Earth would be friendly to the GTVA in any case....Maybe even recognizing them as it's own independant nation and then joining the alliance themselves perhaps? Though history shows nations not wanting to get rid of colonies, hello America. So perhaps they would fight to(peaceful fight) to try and get the Terran part of the GTVA to once again become subserveant to Earth.
I would hope though that they kept the name for the alliance

But, I'd almost be glad that the jump node to Earth was severed. Because otherwise they would still be vulnerable to attack, the biggest Terran cultural achievements are all their and it's their history, and their capital.
Also I think you're all disagreeing but essentially your all agreeing, that destroying the Lucifer destroyed the node and that....wait nvm...I now see the dilemna, perhaps they did destroy the node from the inside to destroy Lucifer that was inside the node...
But anyways, as long as the ship was inside it, whatever ship goes down with the node and the node goes down with whatever ship blows up inside it, so yeah. At least that's how I see things, never played the first FS.