Is it possible in keynote 09 to stretch a line through an animation without making it more broadly?
I would do the animation of the line as a Magic Move. To do that, start with the line on a slide. In the Slide Navigator, duplicate the slide. On the second slide, adjust the length of the line (and position if you wish). Select the first slide in the Slide Navigator and apply the Magic Move transition.
I like using Magic Moves for things like this because it makes it easier to deal with multiple elements on the slide.
If the line ends at the edge of the screen, easy: make the line the full width needed, put most of it off-screen and animate in with a move.
If the line doesn't go all the way to the edge, you'll need to do a similar thing, but with some fakery. Remove the line and take a screenshot of the area between where the line starts and the edge of the screen. Make the line the full width needed and replace to where it should be initially, leaving the tail trailing off-screen. Then, put the screenshot of the background back on the slide atop the line to hide the line's tail.
If you have other animating objects over where the line's tail is, make sure the line and the fake background are below them so they don't intermittently disappear. With many objects it can be tricky, but definitely doable!
Add the line as you want it to be at the end of the animation. Then add a square which is the same color as the slide background. Arrange the square over top of the line so that it is no longer visible. Use a wipe, build out animation on the square to make the line gradually appear beneath it. This creates the illusion that the line is growing.