Over at the Rough Beasts of Empire thread, David raised an interesting question. I think anyone with an extensive history of interaction with the Federation would have been doomed, yes. The powers that sent forces to the Azure Nebula? They'd doomed themselves, and were too close to the subspace aperture anyway. The Tholians? Yes, likewise too close. The independent worlds, the non-galactic powers, wouldn't be--weren't--protected by their small size. How extensive is extensive? Would the Sheliak, on the far side of Breen space, have come under attack? What about the Regnancy of the Carnelian Throne, say? There was a Caitian colony near their space and a certain amount of long-distance trade and even skirmishes with the Federation. The Mabrae? More distant cultures? Bajor might survive. If the Iconians were [strike]so terrified of the Prophets' power[/strike] respectful of the wise Prophets that they stayed away from the Bajoran system, the Prophets might be able to deter the Borg. "You are not of Bajor." Whether they do, that's another story.
If the Borg hadn't have been absorbed/defeated in Lost Souls and David Mack (and others) had led the Borgs invasion of the Alpha/Beta Quadrant to it's most logical outcome. I suspect they wouldn't have stopped. They may very well have given time, destroyed the entire Federation, it's allies, it's enemies and then for good measure, spread out further and annihilated everything in this part of the Milky Way. Maybe a handful of ships would get out, but as the collective was hell bent on destroying all of Humanity and the Federation. They would have pursuded them and would more than likely destroy everything they touched.