Can someone tell me how long it typically takes for Fantastico to integrate the new WordPress version?
Well, Fantastico won't have WordPress v2 now, because it hasn't been released yet. Once a new version has been released, the Fantastico team "checks it for quality and compatibility" and finally adds it to their repository. From that point, it all depends on how often your hosting provider synchronizes with those repositories. So, I guess that it would take anywhere from a week to six months.
There have been some reports here of problems following Fantastico installations, and the manual installation is quite easy, especially if you follow a good guide. I always recommend manual installations over the use of Fantastico.