Jimmy, if the entire Empire, including resources from the provinces of Morrowind (Vvardenfel devastated by impact and eruption, mainland reeling from Argonian invasion), Hammerfell (beat back the Dominion alone), Blackmarsh (strongest it's ever been), Elsweyr (Skooma cats be cray-cray), and Skyrim (functioning at full bore and united), can't take the Aldemri Dominion, then how in the name of hell is Ulfric's army, which has failed to actually defeat the Imperials at all until the Dragonborn gets involved going to take them on? He's shooting himself in the foot with his racist attitude, shooting himself in the foot by dividing Skyrim, and it all doesn't matter because the Thalmor will literally just remove him if he becomes a problem for them.
Only the Empire stands a chance against the Dominion, Ulfric is just a puppet and cannot ever be anything more. Not to mention that even when he does do things his way, it just turns into a merciless bloodbath (The Reach anyone?)
Edit: Forgot Orsinium in there, but from what I understand they were pretty much a non-factor in the war.
Elsweyr didn't support the Empire, the Khajiit became vassals of the Aldmeri Dominion in 4E 115 when the Elsweyr Confederacy dissolved, a full five decades before the Great War.
Black Marsh didn't support the Empire, the Argonians seceded from the Empire after the Oblivion crisis and are neutral to the conflict.
Morrowind isn't mentioned as providing any significant support to the Empire during the Great War in 4E 171-175, which is pretty consistent with them having their province blown up recently.
In fact, the Aldmeri invasion was countered mainly by three forces. The Empire itself throughout the entire war, Hammerfell which focused on defending its own lands once the Empire retreated, and Nords.
It was the force of Nords under General Jonna that assisted the Empire at the Battle of the Red Ring and were the ones that successfully turned the tide of battle. It was the Nords that carved their way from Cheydinhal to the Imperial City in two days, then held the road and slaughtered the Aldmeri reinforcements while the forces of Titus Mede II retook the city. It was the Nords who, after a long and bloody battle, turned around and went home to discover a bunch of provincials had taken the opportunity to seize control of Markarth. Can you blame them, with the memories of the Battle of Red Ring still fresh in their minds, for going in and putting the uprising to the sword?
From this we know that there's really only three armies equal to the Aldmeri in strength and allied against them: the Redguard of Hammerfell, the Imperials of the Empire, and the Nords of Skyrim.
Now even though the White-Gold Concordat meant Hammerfell left the Empire, we know that they are still capable of holding off the Aldmeri Dominion on their own. Why wouldn't the same be true for Skyrim?
Honestly, I see only good things coming from Ulfric Stormcloak sitting on the High King's throne. Yes, the man's a bloodthirsty bastard, and honestly that sort of man is exactly what is needed to smack down the Aldmeri Dominion. Especially since some
Dark Brotherhood asshole went and assassinated Titus Mede II, throwing the Empire into further chaos.