Let's say I have a MOSFET already operating in saturation such that Vds > Vgs - Vth. Can I make it to operate in triode or linear region by simply varying the drain voltage such that now Vds < (Vgs - Vth) where Vth is the threshold voltage for MOSFET to switch on??
Yes. See picture above. Let's say that Vgs is Vt + 3V, and Vds is 5V. The MOSFET is in saturation. If Vgs stays constant and Vds decreases, it corresponds to a movement following the curve and moving toward the left. If Vgs stays at Vt + 3V while Vds decreases to 2V, the MOSFET is now in the ohmic region of operation.