Some of the movement I'm seeing in those arrows would probably be better done in a dedicated 3d program (which is likely how the rest of this illustration was built anyway), but if you're ok with toning down a little bit of the 3d twists and turns, you could absolutely do this in After Effects.
I recently released a free arrow preset that could get you started: https://gumroad.com/l/LNSVU You'd be able to edit the path the arrow takes and move it along that path to meet your needs. If you're in need of the flaring tail the arrows in your example have, check out some of the new Taper options within the Stroke settings for the shape layer.
Since this is built on a shape layer, you'd also be able to apply extrusion using the Cinema4D 3d renderer.
Let me know if you need additional guidance on any of that! I usually try to start with breadcrumbs so people can discover and explore the tools themselves, but let me know if you get stuck.