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You may be able to attach a 3Doodler

You would need to move it (or the print) on the z-axis as well. And printer heads are usually quite big and heavy, I'm not sure if they can get small enough for this.

The Piccolo seems to be a 3-axis machine, i.e. it can already do that since lifting the pen is quite essential when drawing.

However, I guess it can't control the extrusion rate dimension that a 3D printer has, so it would still fall a bit short.

Use the CNC to move the stage, not the head.

Look at the spiral it's drawing. It has way too much play, like several mm.