Just to stir the pot, ;-)
When I hear "capacitive transducer", I think "capacitance as a function of x", usually x being (direct or acoustic) linear or angular displacement, humidity, ionic, etc.
A variable capacitor, biased from a polarizing voltage, will indeed generate a signal, but the signal from, say, a 100pF air variable being turned a few degrees at 100Hz, is microscopic. Trying to measure changes in humidity by the change in voltage, at constant charge, is absurd.
Acoustic transducers with external polarization (rather than electrets or peizos) do work reasonably at high frequencies (10s-100s kHz), which would be more what we're talking here, but I'd hardly call such a source "no signal", even though it might be mV, even uV ripple out of a V bias. It's simply what it is. The voltage might even be much weaker than the air variable's case, but because the frequency is higher, the impedance is lower and easier to deal with.
Most of these transducers, in any case, are measured parametrically, with an RC or LC oscillator, or a C bridge, where the signal is stronger or easier to detect (frequency measurements being the most accurate method available).
Tim