Your operating point in closed loop depends on the load
current demanded and VIN-LOAD headroom. The Vgs
will be swung to get that current - or peg low and still
fail. But this is the dependent variable, asserted by the
control loop to make the feedback right.
The gate drive from amplifier needs to be rail-rail output
capable to get both minimum leakage / best Iout(min),
and maximum output current / minimum dropout voltage
at low line.
Make it easy on yourself and break this down to its
simplest case - min line, max load, Vgate=GND will
tell you all you need to know about the pass FET
drive; max line, min load, Vgate=VIN will tell you
about leakage (to the extent that your model is
realistic, there).
If you can't make it at these two cases then the rest
of circuit design has nothing for you and you need a
better (could be bigger, could be smaller, could need
better process) pass FET.