Unfolding and exporting meshes with textures


I’m desperately trying to export unfolded, undistorted meshes with their textures on top. I have an add-on which unfolds meshes with zero distortion, in order to make paper models, but it exports only the tris and quads of the mesh without textures. I’m wondering whether Blender will UV unwrap an imported mesh in an undistorted way if that mesh is a developable (curved in only one direction) shape. If so, then I can just use the textured UV map to make my model, provided I only import developable surfaces (importing the meshes is a vital part of my problem - I use other software to design the developable shapes). Or maybe I can plan my seams on a complex model carefully enough that all the parts are themselves developable - although I don’t want to face that prospect. Can I count on Blender to accurately UV unwrap a developable surface?

Thanks for your consideration