In ASOS, Robb tells Catelyn, that he cannot send her father to treat with Renly due to his condition. If Hoster Tully is healthy and is able to make the journey to Bitterbridge, does that change either the tenor or the outcome of the Stark/Renly negotiations?

Tricky question. 

If Hoster is healthy and able, Robb has thousands, possibly tens of thousands of more men under his command, and the Lannisters quite possibly get beaten outright during his initial campaign, rather than half beaten. 

This changes the political and strategic dynamic immensely. If Jaime and Tywin are captured or just knocked out of the war due to crippling defeats, then Robb could potentially make his own drive on King’s Landing to rescue his sisters and avenge his father’s death himself. Moreover, if Robb’s in a stronger position, Tyrion might make a deal just to get the armies back to save King’s Landing. 

So Robb might decide that he’s achieved his war aims – Lannisters beaten, family united, honor upheld – and decide to go home. Maybe he does that as the King in the North, although I think Hoster would have steered the war council away from that, or maybe he just says that he’ll bend the knee to whichever non-Lannister takes King’s Landing, send him a raven.