I just don't believe they can. They are basically only half of Skyrim and even if them winning the civil war became cannon, it's still only Skyrim by itself against basically the 2 provinces of Alinor and Valenwood not to mention they would probably get the Khajiit to help them out too. When the great war happened the Empire had Cyrodiil, Skyrim, and Hammerfell and they still lost so Ulfric would need to make some allies if he wants to win against the high elves. I don't see him caring about other provinces if they did manage to get the Thalmor out of skyrim.
As for the second thing, the Thalmor did also get weakened during the war which benefits both sides but as far as I'm concerned a reunited Skyrim along with Cyrodiil would be the best bet for a victory. The ideal situation for me would be if Tullius and Ulfric both pulled their heads from their own asses and allied to get rid of the real threat but that wont happen lol.
Yeah, it doesn't make sense to me how four provinces couldn't win the great war but one province, or two, could win the next one. And even if Ulfric wants to take the fight to the Thalmor, what if his Jarls or his people just want to rebuild after the war?
And the Thalmor are in much better shape than everyone else. Most of Cyrodill and Hammerfell are devestated and are still recovering after the war. And Hammerfell, home to the greatest warriors in Tamriel, still took five years before they could agree to a truce with a weakened and demoralized Dominion army. Alinor, Valenwood, and Elsweyr are perfectly fine by comparison.