The device is turned off, there is no channel. so yes you will have a constant cap but the cap is now a Gate to Body cap, which is very small. essentially like having a small strip of poly over nothing(think parasitic cap). for the device to act as a good cap, you need to make use of the very very small gap between the gate and the channel (the very think fox layer separating the two). to do this you need the device on, but as mentioned if the device is on and in subthreshold region the cap is heavily dependent on Vgs.
-Pb