Slicing software and Sidewall
Just for the fun of it and perhaps to contribute to this question, I opened my recent task in Simplify3d slicing software. Setting the perimeter walls and top/bottom surfaces to zero did not generate an error as I expected.

The print preview, essentially a g-code viewer, presented the model as only the honeycomb infill for which it was configured. Having zero layer thickness for the top/bottom also prevented features from printing that were composed of only walls without infill. Small details that otherwise print well were lost completely.

I can see that properly designed models printed with certain infill patterns and percentages would be quite artistic.

With respect to the first question, one could create a program to accomplish the desired result if one were an experienced programmer. It would be a matter of converting a specific set of vectors into g-code for the printer. I'm familiar enough with g-code to know that a well defined curve is easy enough to create in g-code but only if the mechanicals support arcs. If not, it's not so easy. The conversion from a vector format file to g-code would require a talented programmer indeed.

I suspect there are talented programmers "out there," but one must be suitably skilled and equally suitably motivated, yes?