Actually I think it could be quite relevant. The mere fact that origami doesn't allow cuts is what makes this so attractive from a texturing standpoint.

From what I can tell, it appears that there are many locations where the original plane overlaps. If it is possible to easily calculate adjacency for those triangles, you would be able to properly do filtering lookups.

Another question is how much overlapping there is. The more there is, the more you potentially waste texture resolution.

Still, cool idea...