Duke Leto was very well aware of how the attack against his house would take place. He even predicted the Sardaukar troups disguised as Harkonnen and that he would die.
My question: Could the Atreides have won if Yueh hadn't sabotaged the house shields? ("Won" in the sense of "ward off the attack") If I understood correctly, the attack was too large and too early, i.e. before Fremen troops could be recruited.
Or was Yueh's role only to ensure that the Duke and his son were captured (alive)?
You are correct in your assumptions: Yueh was tasked with two things only: capturing Atreides ruling family alive and deliver them to Harkonnens intact...
And yes, Thufir Hawat himself says that the force brought to the fight by Harkonnen was overwhelming. If I remember correctly the numbers of attackers were in the range of 100 to 200 times of those expected by anyone. Also the intelligence possessed by invaders basically assured their victory, even if using much smaller forces.
Without Yueh's sabotage the attacker losses would be much higher and there was a high risk of the Duke and Paul to die in fighting. That they were to be unharmed was the condition of the Emperor and why he was used at all.
Baron Harkonnen, while watching the attack, notes that his weapons are old-style kinetic artillery, not the modern energy-based ones, and thus bypass the shields. Elsewhere Harkonnen claims that subverting Yueh was nothing more than habit.
But the baron rarely tells the whole truth. He broke Yueh's imperial conditioning because he found a way to do so. The fact that it had never been done before, that allegedly it couldn't be done, made it a challenge. Unshakable integrity, to the baron, is like a vacuum--it shouldn't exist. Yueh became just another Harkonnen asset, all the more useful because he was above reproach.
Was Yueh's interference critical? There's no way to be sure. Leto might have died in the attack. On the other hand, without being able to count on Yueh, Harkonnen might order his troops to advance more carefully, regardless of the cost to themselves, and take Leto alive. No doubt the baron had other contingencies in place. Of course, if Leto and House Atreides had survived the attack, the rest of the story would have turned out differently.
For literary purposes, however, Yueh is all the more tragic because his betrayal means nothing. His wife is already dead. Deactivating the shields doesn't change the outcome. To the baron he is nothing but a loose end, a tool that has outlived its usefulness, fittingly stabbed in the back.
According to the way war is waged in Dune, the impact is gigantic. In the David Lynch movie, they estimated the impact to be equivalent to 10 sardaukars legions.
Add to that, that Atreides had the second best military power and was rapidly catching the emperor... If the Atreides were not destroyed overnight, it is not impossible that fremen would have lend a hand. And they inflicted huge losses to the harkonnen army even before the arrival of the Atreides. Also the longer the war, the more likely the emperor hand in this would have been exposed.
