I would imagine that there would be a lot of problems fitting a fully functioning theremin to a guitar body and being able to use it for both a theremin and a guitar. As mentioned above. The strings are grounded, and the strings ground every metal bit from the tuning machine heads to the Bigsby vibrato tailpiece, and the guitar player himself. This is common with all electric guitars. It is done by wiring the anchor of the bridge to the shield of the output jack. This reduces a lot of 60 cycle hum that would normally be picked-up by the guitar. So the Bigsby's handle is grounded wich wont work for a theremin antenna. You could somehow isolate the handle itself using some non-conductive bolt and washer, but still the antenna would be in very close proximity to something that is grounded, which would probably change the tuning of the antenna to the point of being un-usable.
Then if you are also using it as a guitar you have the issues of your hand strumming strings near the antenna, which may or may not be a noise you are looking for. Worst though would be that guitars are typically only 2 inches thick and your antenna would be pretty close to your hip or stomach all the time.
I have seen optical theremins mounted on guitar though, and they don't have any of these issues. But they also don't look like a normal part of the guitar either.
