Can this VCA bring output volume to zero?
The JFET channel resistance is the limiting factor for (close to) zero output. 

By ensuring that the JFET channel resistance is &lt;&lt; Rin, you can get very close to zero output.

As it happens, I am using this base circuit in an ultrasonic pre-amp:



It has this control voltage:



and this output response:



I am using MMBFJ177 devices in the actual application and the circuit output goes down to a few 10s of microvolts.

The maximum gain you can get is a bit dependent on the pinch-off voltage.