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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??

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enter image description here

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.

Image source: https://allthingsvlsi.wordpress.com/2013/04/04/nmos-and-pmos-operating-regions/

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keep in mind how short channel FETs are poorly described by the standard long-channel equations we are taught.

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