system
Given the following post, respond as if you're commenting on Reddit:
human
[Game of Thrones] Had Robb been informed of House Bolton or House Frey's treason, could he have won the war?

Assuming of course that either:

A) At Harrenhal, Brienne decides to warn the Starks of Roose's new friendship with Tywin and refusal to send Jaime back to Robb (via undetected raven)

B) Messages between Tywin and Walder Frey reassuring recompense for the Red Wedding plot are intercepted by someone loyal to the North (or say, Littlefinger who wants to save Cat)

Do either of these play out better for Robb than the established plot?
gpt
Probably not. We're told that the Stark army is running on fumes through the show and it's only Robb's (and Roose's) tactical genius that is allowing them to punch above their expected weight (and also that the North is like *really* hard to invade). Roose flips because he sees the writing on the wall and doesn't like that Robb won't play politics to win the war. Here is probably what happens

A) Robb gets the letter warning of Roose's betrayal. Robb confronts Roose. Roose either convinces Robb that the letter is a trap designed by the Lannisters (and then the story plays out as usual) or Robb kills Roose. Roose's Bannermen go home and Robb is left with even fewer troops and the loss of a good general (this doesn't even take into account Ramsey). Robb doesn't have the army to march South. The Lannisters use their perceived wealth and the Tyrell's food surplus to marshal their forces and eventually crush the North. Only caveat is that if this takes too long and Tywin is killed then maybe the Cersei's invasion goes poorly. Robb isn't going to bend the knee to either Dany or Stannis, meaning neither are as willing to support the North's defense against the dead.

B) Different path, same results. Robb was allying with the Frey's to get access to their lands (a huge strategic point) and their troops (who, IIRC, were the only neutral power of note left). Even if they dodge the Red Wedding, they still don't have the troops needed to take the fight to King's landing. Frey allies with the Tyrells. Above plays out as before.