Only about 40% of the population that got involed supported them, and the Empire had home-field advantage and still lost hard. The Stormcloaks would be massively outnumbered, alone, and wounded from the civil war. Besides, Galmar said he was going on the offensive and invading the Summerset Isles.
The Empire's land is nothing like Skyrim.
The “Skyrim cannot survive alone”-argument
This one is one of the simpler arguments to debunk, because any high school dropout can look at the map and see how silly this argument is. Here. http://www.google.com/imgres?imgurl=http://cloud-2.steampowered.com/ugc/918987149705159097/C22C10AE7A645DE484D4521251914E3138836D83/&imgrefurl=http://steamcommunity.com/sharedfiles/filedetails/?id%3D91249786&h=1202&w=1861&sz=93&tbnid=nBGo07R-Omi71M:&tbnh=90&tbnw=139&zoom=1&usg=__7BIkCEpKVKwWqHJ0jtswf0XmBMU=&docid=Tpko8a8T0KYY3M&sa=X&ei=l3tIUd2vEIyy8AT6zYGwCQ&ved=0CDUQ9QEwAA&dur=1510
Lets look at the two ways a military force can invade a territory. The first possibility is by Land. If the Thalmor were to attempt this, they'd need to go through either Morrowind (not allies of the Thalmor, and never have been, plus Argonians occupy part of it and are fighting the Dark Elves) or Hammerfell (obviously hostile to the Dominion) or through Cyrodiil. Now many say that there's the solution. The Thalmor have a treaty with the Empire, and they are allowed through Cyrodiil and Skyrim. Two things. One, the Justiciars are allowed, and two, whole armies are clearly not. How do I know this? Tullius himself says at the Empire is currently guarding it's border to watch for an attack from the Dominion. Think about that for a sec. If the Thalmor were allowed to walts in whenever they wanted, why the hell is the Empire wasting their time guarding their borders? It makes no sense. Clearly the deal of the Thalmor in their territory extends solely to Justiciars for hunting down "heretics" not their whole army.
Now look at Skyrim's natural barriers. Mountains. The worst kind. You cannot sustain an flow of troops and supplies through a mountain range. Not easily anyway. Couple that with the intense weather, and you have a complete supply chain disaster. Now, the Thalmor, assuming they actually did get through Cyrodiil in whatever fashion still would have trouble getting through even if they used the Pale Pass, due to it's treacherous reputation. Here's an example of how it caused trouble for Tullius during the Stormcloak rebellion:
http://www.uesp.net/wiki/Lore:Pale_Pass#cite_note-4 In http://www.uesp.net/wiki/Lore:Fourth_Era#4E_201, the Pale Pass was closed due to avalanches, preventing Imperial reinforcements from helping to secure Falkreath Hold under Imperial control during the http://www.uesp.net/wiki/Lore:Stormcloak_Rebellion.http://www.uesp.net/wiki/Lore:Pale_Pass#cite_note-5http://www.uesp.net/wiki/Lore:Pale_Pass#cite_note-6
In short, a land invasion is highly unlikely in the current situation. I didn't even talk about the obvious disadvantage of fighting in a cold climate that the Thalmor are not at all used to fighting in (their homeland is SUMMERSET ISLE for Talos's sake) against a people who are literally magically resistant to cold weather and magic.
Now lets look at what the Thalmor are actually good at. Naval invasion. The Thalmor are known to have the most advanced and powerful naval force in Tamriel. But even the most advanced naval ships cannot successfully invade without a safe port nearby to house reinforcements and supplies to sustain the attack. See how far away Summerset Isle is? It would be comically impractical to invade Skyrim from this far away, whether that be by land or sea. Even our real life history proves this fact to be true. The Thalmor can't set one on the coast of Skyrim to the North because one, they'd be under constant attack, and two, the Sea of Ghosts is as the name suggests extremely treacherous. They don't have any islands nearby to do this either. The only possibility they have is to anger the Dark Elves as well, and take one of those islands that are literally on the opposite side of Tamriel from Summerset Isle. Then they'd be fighting two nearby nations at the same time, and this time one of them is magically adept, and are as tough as the Nords are. So without a true safe port, this invasion tactic is even more unlikely to succeed.
This is why I personally laugh at those who say "without the Empire in Skyrim, the Stormcloaks are doomed." The Nords could literally sit back and gulp down some Black-Briar mead while the land does the fighting for them.
Now, as for the population who support the stormcloaks, a few things.
1. After the Empire's kicked out and all the Jarls are stormcloak, it wouldn't matter. The nobles would fall in line out of necessity. Same is true if the Empire wins. Its the same situation.
2. They wouldn't care anymore after tha Thalmor attack.
Now for actually attacking the thalmor not defending, it wouldn't matter who won in Skyrim. The end result is the same. Cyrodiil Hammerfell and Skyrim will all become allies out of necessity against the dominion. That seems inevitable. Thats likely why the dominion wanted the war to continue. If the civil war was going on while they attacked, an alliance would be impossible, but now that Cyrodiil has no choice but to accept Skyrim's independence, their only choice is to not ask to be allies, and burn, or to ask and live.
Now I know both Skyrim and Hammerfell dislike Cyrodiil, but they'd have to help them, because if Cyrodiil falls, they're next. Plus, the war would stay out of their provinces, and their infrastructure would stay in tact.