Vince was important to show how desperate Austin was. From what I got of it, he spent a year out with injuries and he was older than he was in 98 and 99, so he wasn't sure he could beat the Rock again. The self doubt thing makes perfect sense, especially when you think about him retiring a couple of matches after his title reign because of the same injury. Plus since he was getting old and the neck injury was wearing him down, he MIGHT never get another shot like this. That's why he needed it more than "anything else in the world".
The turn made the match. For 40 minutes, you see his frustration build up, how nothing he could do could put Rock away, and he just couldn't beat him. Realizing that or not wanting to take the chance, he uses his backup plan, Vince. The chairshots by itself wouldn't be enough. Austin used chairs in a lot of matches. But siding with the evil boss, going against everything his old character stood for proved how obsessed he was with winning it.
Now they were in texas, so nothing they could do would turn the crowd against him. But to everyone else it was a heel. Aligning with Vince was about the only way he could have turned heel.