It does now occur tome that pretty much all of their stuff on this topic is in the Imperial era - so, in fairness, it hasn't happened yet in terms of explicit stuff. But in simple terms Corellia ended up going in with the Empire (which is what led Garm Bel Iblis to start his resistance group), and in any case was generally fairly pro-isolationist despite the longrunning history of firing off colony missions everywhere. It was better than many or even most of the Cor human worlds since it was one of the few that still allowed alien workers by 1 ABY, but it's still fundamentally pro-Palpy for most of the war. Case in point, Corellian as a term is usually only ever applied to its human population, regardless of if any non-humans have been living there their entire lives. Additionally, Corellia polices the other worlds in its system over the heads of Selonians or Drall. It's hardly Pius Dea type stuff, but there's this consistent subtle undertone of supremacism.
My source for this, to save searching through lots of books, I'm going to use Coruscant and the Core Worlds (2003).
Now, I do concede I forgot that all of this is several thousand years away from happening, but given Corellia's more or less total absence from KOTOR era mentions, and how Core human major powers that aren't Empress Teta typically go... yeah I don't trust that Corellia won't go that route. In any case the Core (human or otherwise) is powerful and influential enough, and even if Corellia was a golden bright-eyed innocent, I would still be firmly opposed to any major Core world being encouraged by the Jedi to expand their reach in any capacity. We should put these kinds of efforts into more rimward worlds, or at the very least Core worlds that aren't swimming in prosperity and power, and especially the ones often neglected by the Core-centric focus of Galactic Republic politics.