You would need a 4th axis to run the extruder head. But there is no reason that it couldn't be done. I think Mach3 will run a 3D printer. I would say that any program that would run a 4th axis would run a 3D printer.
This is on my to do list, I have a parts list around here somewhere.
There a few things that good 3-D printers have in addition to the XYZ and Extruder motor control. You also need a heated bed and contained space around the print to prevent drafts and allow for even and controlled cooling of the material. Some materials are more sensitive to this than others.
It has been done. I looked into the Mach3 forum it can be done but is it worth the time and effort to me? Probably not. I was thinking about pattern making for casting. Made the 3D model, cast one in aluminum then you have a more durable pattern. A dedicated wooden one would be easier to make for me. Nothing new to learn. Wooden patterns have served the old sandcrabs well.