And though the Empire does have recruitment possibilities from Skyrim now, they are still battered from the Civil War and an easy target for destruction. Stormcloak rebels are still running around Skyrim, and could potentially be coerced into helping the Thalmor under the guise of revenge for the Civil War.

However, it ends up as a similar situation if the Empire wins. So, if the Stormcloaks win, Tamriel would most likely end up in Admeri Dominion control. It's an extremely easy target for the Thalmor to defeat and disband. The Empire is also battered, losing it's recruitment of men from Skyrim and having suffered casualties from the Civil War. Secondly, the Empire is now just two provinces: Cyrodil and High Rock, neither of which are connected to eachother in any way, except for by water. So, the Stormcloaks free Skyrim, get destroyed by the Thalmor, and Skyrim becomes another province in the Aldmeri Dominion. The Stormcloaks can barely beat the Empire in it's weakened state now. Ulfric and his sword-and-shield-only men can't compare to the might of an army of magic wielding Elves who have previously taken out the Empire when it was much stronger than it is now.

For one, they lose to the Admeri Dominion, no contest. Skyrim secedes from the Empire and becomes it's own nation. Let's say the Stormcloaks win, regardless of if the Dragonborn helps them canonically or not. The issue is, that with the mere existance of the Civil War, the Empire is doomed to the Thalmor.

Skyrim fight the thalmor