Strokes that complex and plentiful are probably done in a 3D program.
As for your specific questions… what kind of trouble are you having making the stroke 3D? If you have it applied to a solid (WITHOUT the 3D switch turned on) and a camera, you should be able to move the camera around and see the stroke render appropriately.
As for the line getting cut off, it really sounds like you have the solid set as a 3D layer, which it shouldn’t be.
You can take a look at the intro tutorial on Red Giant’s site if you haven’t already.
Regardless, a simplified version of this could be accomplished with animating both the start/end points of the 3D Stroke and the stroke itself. But again, I really feel that this was done in a 3D app as 3D Stroke in AE can get messy fast.
Adobe CS3, Apple FCS2
[Disclaimer: Sometimes I am an idiot and misinterpret people’s posts. I’m sorry.]