Hey,
No.. MOS Digital Circuits operate mainly in the Saturation and Cut-off Regions. Except for the Pass Transistor Logic where it might operate in the linear region.
We use the MOS circuits mainly in the saturation and cut-off regions because at any point in time, we want the output or the voltage at an internal output node be connected to either of the supply rails with a very low resistance to insure strong logic output and increased noise margin.
Sometimes, we have to make trade-offs, but mainly, even in ratioed logic, we want a strong output. So, one of the MOSFETs used must be in saturation to insure minimum impedance.