Path or mesh for 3D printing

[ahp]

Hey all,

I have a relatively simple question. I'm modelling a small cabinet to store pen nibs and for the label of the container I created a vector graphic that I imported into blender. My question is can I keep the label as an extruded curve or do I need to transform it into a mesh for 3D printing? I ask this because the transformed mesh is kind of messy and I'm not sure if that will print nicely?

Attached images:
1) vector as curve (with extrusion in the properties window)
2) vector in edit mode
3) vector as mesh in edit mode