Yes, you will most probably get it producing a sound. But il will not be playable because of a very incoherent tone spacing (un-linearity) and a sluggish volume response. A guy in Germany is producing theremins based on that circuit and selling them on ebay under the name "Golem Theremin".
I've seen many of these "instruments" and many people who were completely disappointed by these, because (even after an extremely long warm-up time and meticulous adjusting) only one single octave in the middle of the pitch range was playable with the established aerial fingering techniques, while the tone spacing was ways too wide below and ways too small above.
Before building whatever theremin circuit or buying whatever instrument, have a look on platforms like youtube or vimeo and check if one of the renowned classical theremin players has used it for a professional recording. If not, keep your fingers away and don't rely on the testimonial of high school students or even engineers without any (at least semi-) professional musical training if you don't want to end up with only a fancy gesture controlled sound or noise generator. Technical data like a pitch range from 20 to 20,000Hz are impressive, but don't say anything about the usable and playable pitch range. If the tones are not widely enough spaced in the high register, you'll never manage to hit a specific tone with precision and a decent vibrato will be impossible because the slightest arm movement will result in a 3 or 4 tones shift.
Remember that the instrument which Leon Theremin built himself for the great Clara Rockmore had "only" a pitch range of 4.5 octaves (from 65 to 1,700Hz), a signal to noise ratio of only 45dB, and a distortion factor of > 10%, thus far below any "hifi" specification, but her playing (technique, expression and timbre) in her recordings are still the reference for every aspiring thereminist today.
