Wow, I didn't consider this. Guess it shows you how much I know about politics. What you say does make more sense. The Empire has no reason to like a Stormcloak!Skyrim due to, as you said, them losing a top general and maybe even their Emperor. All the Thalmor has to do is to strike a deal with them to allow a peaceful crossing in exchange for, perhaps, supplies and more troops. If I were a citizen of Cyrodiil, I would likely be more accepting of the Thalmor marching through my land to punish Skyrim than thinking, "Oh those poor Nords! I should help them!" Couple with the dragon attacks, Skyrim is indeed on shaky ground.

Of course, as BretonSpellsword and Treng mentioned, do we really know how big of an armed force the Thalmor has for such an invasion, even if Cyrodiil allowed them to pass through unmolested? What of Hammerfell and High Rock? From what I've read about the Great War, most of the provinces fighting in that war all but exhausted their supply line and military number.

We've had this argument umpteen times on general forum and every time I show proof you ignore it. For those interested, read the Great War and the book by the High Elf who recounts the war. I don't remember its name.

The Thalmor are defeated. They lack the capability to act with any military might, so they produce the shadow of a military they don't have to try to be master Rooseman. That's the long hard fact of the matter.