Not quite. There wouldn't be any legitimacy of the uprising. "Why are you rebelling against the empire?" "No reason, just to rebel." The banning of Talos is what gave them a rallying point. Claiming he was manipulated by the Thalmor is only true insofar as the Thalmor engineered the WGC to provoke hostility from other provinces.
"Don't ban Talos worship" is their rallying point, though the point that's conveniently overlooked was that people didn't stop worshipping Talos. The Thalmor knew the Concordat was doing diddly squat to stop Talos, so had to manipulate Ulfric into starting the civil war over it. If Ulfric hadn't started the civil war Talos worship would've continued, but now with the civil war Talos worship is being put under the spotlight (causing people who would've continued worshiping him into declaring they don't, like High Queen-to-be Elisif). And hell, Ulfric murdered the High King,
who worshipped Talos, because he supported the Empire.
Both the Empire and the Thalmor know the Concordat isn't going to last, and there will be a second Great War. Starting a civil war over Talos worship actually did more harm to Talos worship than if it had been left alone. In the long run, it probably will all even out, but in the mean time Ulfric is causing internal damage to the forces that could otherwise combine against the Dominion.
Unless the thalmor were foolishly sending suicidal forces into the Empire afterwards, there's no difference between WGC and nonWGC for the Empire's recovery. And I say foolish because the thalmor have troubles replenishing forces whereas mankind doesn't have that issue.
The Empire didn't know the status of the Dominion's forces. They just knew that their own legions were decimated, and none of those that remained had more than 50% of their troops ready for battle. The Battle of the Red Ring was their gamble to reclaim White-Gold and Cyrodiil, it was not a force designed to wipe out the Dominion. You don't just take a bunch of fighting men and tell them "go fight those guys" and expect to win. It takes a lot of information gathering, planning, and coordination, and that's something Titus II didn't have because he was too preoccupied with regaining Cyrodiil.
The Concordat was a temporary peace designed to give them a breather, to gather information and start planning while their troops were rebuilt. Then along comes Ulfric...
The Mede line isn't hereditary. Seems to be picked by the Council or possibly the previous empire. We know that Mede II isn't Mede I's son though.
Is there any proof that it's not hereditary? Attrebus was Titus I's son, but that doesn't mean Titus II can't be his (great-)grandson. It would be odd to have Emperor Titus Mede II who isn't a descendant of Emperor Titus Mede who started the current Empire.
Without the WGC, the empire would be in Valenwood already and possibly even in Alinor
With what? They had far less than 50% of their troops left. You send them into Elsweyr, Valenwood, and Alinor (which is deep in enemy territory, with probably not much intel on them), and Cyrodiil/Skyrim/High Rock/Hammerfell would be completely unguarded. It took Titus II years of planning and preparation to retake Cyrodiil, and you think he can just continue on into the heart of the enemy with no further planning or preparation, when you have less than half of your forces fit for duty?