Can I use antennas as approximate proximity sensors?
Theremins operate on near field effects. There are essentially two antennas and as your hand approaches them, the additional loading capacitance produced serves to detune them. This detuning is detected and the volume/tone are accordingly adjusted.

Near field effects could be exploited for proximity detection, however the distances for effective loading are actually quite small and dependent on frequency. The higher the frequency, the closer the loading object needs to be to the antenna. This implies that a low frequency would be ideal, however any stationary metallic/conductive object within the near field zone would serve to load it. Particularly for low frequencies, if there are existing loading object such as filing cabinets or even daily differences in ground moisture (earth conductivity) the loading will be different. Its a moving target. If the field is loaded with static objects and a dynamic one enters the system, the additional effect due to the dynamic one will be less effective.

Higher frequencies could be used and the shadowing/ghosting and reflections could be measured between the two antennas. Any conductive object within the space which is capable of reflecting/absorbing the field will distort the maxima/nulls of the standing pattern which can be measured as shifts in the received signal strength (RSSI) on both the antennas. The principle is analogous to moving several inches left or right for a better signal when speaking on your mobile phone except the environment is being altered rather than moving the antennas. The pattern will change on a daily basis due to the same effects, however you can determine if an object has entered the vicinity by examining the rate of change of the RSSI on both antennas.