An easier way to think of this is to draw the physical structure of a mosfet and then consider the connections. The total capacitance will be Cgs+Cgd including the oxide capacitance.
In a MOS device, any resistance exists between drain and source whose value depends on the bias (region of operation, Vgs). Here, the drain and source are shorted together to create a two terminal device between the gate and the drain/source. The current in this direction is ideally zero as the oxide is an insulator. Therefore, this device will not function as a resistor.
To make a resistor, you could connect the gate and drain together creating a 'diode connection' with Req=1/gm