Is this style of animation achievable in AE? Or is it safer to go the tradional route to achieve this kind of effect?
After Effects is certainly capable of doing that kind of animation. It's not automatic, but everything saying that example can be accomplished in After Effects.
Yes you can. I'd draw lines using the pen and stroke tool on a shape layer , animate them using the Trim Paths and maybe add the Vegas effect to give some unevenness to your lines. Then add a Wave Warp to each line so they wobble/undulate and finally add Posterize Time (with a low fps, like 3-5), which will give it that stop motion effect. Then add a texture over the top of everything (may need to add Wave Warp and Posterize to this too)... That should get you started, you'll have to play around and experiment as I'm just thinking off the top of my head at the moment!