well, they will very definitely resound to a signal in the millivolt or microvolt range, but this would need to be added to a constant voltage, and the amount of variation would be tiny.
Amplifying that small signal before applying it tho the diode would allow you to change the capacitance more.
The reason you need a relatively large voltage change to affect the capacitance is that you don't want the signal itself to change the capacitance (typically).
If your control voltage was significant at a might change then your signal would need to be even smaller.