I feel like it works as a thought experiment more than an actual campaign concept. The Five Nations are just coming out of a massive century-long war that ended inconclusively, and they all have adjacent neutral territories on their own borders that they've either not tried to conquer, or tried and failed. They're not going to suddenly become buddies with each other, nor are they going to be universally motivated to throw all their forces into a cross-planar war of conquest.
A possibility that might work is if it's not a conquest, but an exodus. If the whole of Khorvaire - even the whole of Eberron - was threatened with a calamity, and the Dragonmarked Houses came up with the concept of spelljamming ships and started cranking them out en masse, then they crammed in everyone they possibly could and blind-navigated the entire fleet to the first material plane they could find, which happened to be Faerun.... then you might have a scenario.