Can carving templates be produced from G-code?
Carving decorative patterns?
If your templates needs to be used like one does a stencil, that's doable... but paper-thin is not as you can't make that with an FDM printer.
But if you allow 0.2 or even better, 0.5 mm thickness, it is as simple as making a vector graphic, importing it into a suitable CAD package, then extruding it to the relevant thickness, and sending it into the printer.
If you really need it to be thinner, invest in a vinyl cutter, and use the same vector graphic to cut a foil template for one use. Upside: you could use the vinyl to etch the patterns in metal.
Carving figurines?
Yes, that's possible too, even easier! Make a 3D model of the finished object in a CAD or 3D modeling software. Either cut up the model right there and export each slice as STL for the printer, or export the whole model and use a secondary software such as MeshMixer to do plane cuts onto the model.
The slices should be at least 0.5 mm thick to allow handling.
It might also be a good idea to use the same model and cut it from a cube, which then is sliced up - that way you get a pattern to press against the outside of the model.