Personally I think it's all perception; if I slowly press down the same switch (my unused Scroll Lock key) on each board, then I notice very little difference on each switch in the feel pushing them down to the point of tactility, and moving just slightly past it.
When I press a Filco brown switch slowly I notice a very pronounced bump whereas when I press a Leopold's it is very subtle. I have read many people reporting that their Leopold feels relatively "mushy" in comparison to the Filco.
Before I was even aware of plate-mounted switches, the first thing I noticed when comparing my Leopold, which was my first mech kb to my brother's Filco was that my keyboard felt different, using "mushier" as the most accurate description that I can think of. From this I can say that I'm sure plate mounted switches do make a physical difference in the typing feel. It is in no way a huge difference, but it is definitely noticeable.