I believe the confusion may come from the fact that in Simscape there is no gravity implied, unless Simscape Multibody is involved. The mass here may be better visualized as a mass sliding on a flat surface, with a spring attached, and a damper (as viscous friction). As you said, the same force will generate a smallver v.der. Because there isn't a load as a result of the gravity, you can ALWAYS push the mass, just at a different rate.
Now, it's possible to add the effect of gravity into this. You just need a force source whose magnitude is -m*g, so the hydraulic force needs to overcome that first.
