No, FastHenry does not work like that. It keeps the input geometry only for the duration of the simulation. You should generate a different input file every time you want to change the geometry. Actually, if you already have a MatLab script to generate your geometry, it should not be difficult to make the script generate also the new geometry with a new value for a geometric parameter.
I also confirm that FastHenry2 can be fully controlled via Automation, including retrieving the results by any Automation capable program (and this includes MatLab).