it's close, but I don't think it will work as is.
one thing I note right away is that for the discharge cycle, doing an alalog.read will not discharge the cap in time for the next cycle, since an analog read only uses microamperes of current (it's a high-impedance input by nature). You'd actually have to do a digital.write (pin, LOW); to drain the cap through a pin (digitalWrite(pin,LOW) places the pin in Lo-Z mode).
In that case you will definitely need a resistor, or you risk burning out the input.
Why not just go with the basic principle of the Theremin: detecting frequency variations? Find a F to V chip that will do the trick and then do the voltage analysis in software.
Have you seen this site?