Think I may have figured out a way. If you enable "use UV for mapping" you'll copy the curve U/V coords to the UV map of the beveled object.
You can then use the vector transform node to strip off the object transform:
AFAIK this will fail if any of the curves have been transformed in edit mode since it relies on the object transform to get the coords back to world space.
Not sure if this is the best way, but I think any solution would have to be based around the "Use UV for Mapping" function as I don't think Cycles has access to the path itself, just the beveled and tessellated output mesh.