There's no real easy way to do this in AE directly. You could use Illustrator to create your paths and then reveal them with a track matte. You could use a particle system like Particular to deposit custom shapes along a path. You could use echo. Do you want to bend the paths after they are revealed like a snake or just reveal the pattern on a path? It makes a difference.
The last option would be to draw a path in illustrator, expand the path with the pattern brush, un-group the expanded path, release to layers, move the released layers to the top of the layer palette, then open in AE as a composition and sequence the layers. Something along the lines of my zillion year old tutorial on morphing Illustrator shapes in AE. You'll find it here.
Well, first of all thankyou for your answer.
What I'd like to do is to animate pattern along line just like a snake. I want the horizontal lines to be stretched/rotated/morphed along the line I'm drawing.
Nice tutorial It may be useful.
Here's a thought: don't use Illustrator. Use AE text, and animate it along an open mask path. I'd imagine the letter I or l in the proper typeface and point size would work very well.