Though, again, I'm pretty sure there is a campaign in the works, and it'll probably be worth playing, consider the difficulties: do you start with zero research each mission? Why, from a storlyine point of view? And if not, then what about the entire research element of the game?
Do you colonise from scratch at the start of each game? Why, from a storyline point of view? And if not, what about the entire expansion element of the game?
Do you, as TEC, need to explore the map at the start of each game? Why, from a storyline point of view? And if not, what about the entire exploration element of the game?
When the Advent and Vasari turn up, why do they need to research and build warships? Don't they already have fleets? They are invading, after all.
Heaps of the 4X elements of Sins make no sense in a storyline campaign. So is the game is reduced to "mash known forces together over and over and over"?
Well no, there are ways to do it, but it'd be hard. Look at the GalCiv campaigns. It's a 4X, and they have a campaign that preserves all the elements of a 4X - but the problem there is, it sucked horribly. Can it be done in Sins? Maybe. I think it'd be pretty cool to have, say, a fully developed TEC civilisation, but with no warships at all, when an Advent invasion turns up. Perhaps a mechanic to "scrap" merchant ships, to convert into warships, or a process to actually strap guns onto the previously merchant-only capships. Maybe have a fleet retreating into the rim, to colonise around the pirates - that'd let you explore and expand in a storyline context.
Vasari might only be able to send the Evacuator alone in an intergalactic jump, tasked with grabbing a foothold and building gates to let the rest of the fleet come over. Research could be seen as simply rebuilding the capacity to construct known designs.
Advent is hard. They arrive with all their tech, all their ships, in an invasion. Perhaps you could have a splinter, cut off by the Vasari arrival? Or a scouting force that discovers Awesome Magic Device X that needs to scramble to build up industrial capacity to beat the other factions trying to get same.
...but in each and every case, what do you do in the second mission? In the first you research, build, expand, explore, develop, win. Then what? How do you reset for a next mission? Why are you starting again, again? How fast would that seem contrived? Tech tree limits always seem fake, and make the game feel like a bit of a drawn out tutorial. But unless you limit or reset them between missions, you'll just be playing with cruiser fleets every game.
So maybe it can be done, but I think there's about as much potential in - perhaps player made - scenario maps. Link them with a storyline, set each up to fit, perhaps use some triggers, and there you are. Campaign.