That the thing, it was the damm nords who started the empire, they disgust me, the nords were originally one of the mede family's supporters, and when he does one decision the back out, as alvor said "Nords have never been fair-weather allies".
In the history of the 4th era it says that Skyrim accepted Mede as emperor after he had conquered his competition in Cyrodiil. That sounds like Skyrim approved it after the fact.
Alvor's words are pretty ironic considering that the empire is selling Skyrim out as it did to Hammerfell, to save Cyrodiil's skin from the Dominion.
Should it? Definitely not, if it wants to have any hope of throwing off the Thalmor. Realistically, Skyrim has no chance to withstand the full might of the Dominion; both the Sword and War Axe, and the Cloak and Dagger. The Empire barely withstood it, what hope would a lone province have?
Point being the empire didn't withstand it- although they may have if they had pressed their advantage after Red Ring. Instead, Mede blinked. The redguard, on their own, did withstand the Thalmor. So, you were saying...?
All that beside the fact that the Stormcloaks do not intend to fight the Dominion alone. Ulfric and Galmar are already reaching out to Hammerfell and High Rock as of game time. Cyrodiil will have to make common cause. They don't have to be the ones in charge.
But of course Beth will make sure to cater to the Stormcloak fans, having them somehow being able to defeat the Thalmor without the full might of the Empire alongside it.

Or, you know, you could just be wrong. For one thing, if Talos is sufficiently weakened, then none of it will matter. So it's not just a matter of mathematics. This is Tamriel and the mythical is usually the more important factor. Talos worship having free rein where it is strongest, the Snow Tower free and not beholden to the crippling WGC, a patch of ground that would be almost impossible for a foreign power to hold even if they took it... That is not something the Dominion wants to see happen. It's in Ulfric's dossier, so you can take it from them.