Certainly the Dominion would view Alpha as a greater threat after the first war than before it. Yes, they would very much wish to win a war of conquest. But if that isn't an option (and a repeat of the first war does seem out of the question), they might well try a different approach for eliminating the Alpha threat.
And they have a pretty frightening quiver full of approaches. We never learned whether a blood test would really reveal a Changeling, or if a "Homefront" style phaser trap would, or if that doohickey from "Apocalypse Rising" would ever have worked - so infiltration remains a possibility as long as there is any traffic through the wormhole. And with infiltration, the Dominion could bring a range of threats to bear. We have seen bioweapons, assassinations, sabotage, nova-bombing... After a short period of preparation, the Dominion could take out the entire quadrant at once with the push of a button, really, triggering all sorts of genocidal devices on the major planets and their stars.
There might be a war then, against a pre-decimated Alpha. And contrary to their usual MO, the Founders might decide not to spare any Alpha lives for servitude, having seen the magnitude of threat they present.
Timo Saloniemi