theoretically, it could do something bad for Skyrim
Added 13 minutes later
and if the Dominion (let's call the 6th installment that) takes place in Hammerfell, it would be more logical to make the Stormcloaks the canon side. like the Altmer went to subdue Ulfric through Hammerfell, and the massacre begins there. something like that
1) Their goal was the civil war, and they don't really need to subdue Ulfric. They just need to show up and finish off the remaining ones. And ideally, start a new war with the Empire.
2) Making the Stormcloaks the canon is illogical. As I said, they act as a "villainous" organization, and that's rarely made canon. Besides, Skyrim under Ulfric's control practically poses no danger; it will only be a war-torn land where there are practically no normal armies left, and many fortresses have been destroyed by both sides and by dragons. An easy target, not a source of threat. But the Empire, which has maintained its unity, is much more dangerous, so the ending for the Empire is more like canon.
3) Hammerfell is not yet under the Dominion's control. And, if I remember correctly, it is hostile to it. Why would they go through another province just to wage war with one province? The war with Hammerfell was quite difficult for the Dominion; they are not idiots to step on the same rake again.