YouTube: CNC Machining a Fender body
YouTube: Making Guitar Neck on CNC Machine
Short Answer: Yes.
Long Answer: Yes, as you can see for the YouTube videos it is done all the time. Try searching YouTube for "cnc guitar" and tones come up.
However, crafting a musical instrument like a guitar is one of the more advanced projects you can attempt. It combines both several challenging CNC process as well adding the complexities of wood, grain and overall design to get a good sounding instrument.
Like SergioPagoada said. If you buy the neck and electronics and just focus on the body a lot of the issues go away.
First you will probably will want the fully loaded configuration. Larger work area, stronger motors.
You will then need software to generate the g-code. For a "Flat" guitar body 2.5D software like Easel should work, but if you want curved surfaces (like in the linked videos) you will need a full 3D program.
Finally you will need a 3D model. Making your own in Easel should be easy enough, but a full 3D model will have a much higher learning curve.
You will need to master 2 sided machining. That is carving the top part, flipping the work piece over and carving the back part. It is not that hard to do, but it does take a bit to get the hang of it and to get everything to line up. I recommend lots of practice on smaller test projects until you get the hang of it. And then doing a test carve with some cheep wood before the final attempt with the expensive stuff.
So I would not attempt to make a guitar as your /first/ project. It is something you will have to work up to. But once you have mastered the principles you can start making some incredible stuff.