Source potential for MOSFET with grounded substrate
In your first circuit, there exist "body effect". But if you can omit that effect



$$
v_{GS} = v_{DS} = V_{dd}-V_{s}\\
v_{DS} &gt; v_{GS} - V_{TN}
$$

It should work in saturation region. Unless \$v_{GS} &lt; V_{TN}\$, \$v_{DS}\$ can't be zero.