Given that most damage in a crash close to the ground is caused by the torque of the blades stopping or impacting the frame of the helicopter and/or ground, no, I don't think it makes much of a difference what you crash on. If the blades hit anything hard enough to stop them, there's going to be damage to the head and more.
Now, if the helicopter were to stall mid flight and blade inertia was lost while in the air (i.e motor failure with no chance of an auto-rotation), then yes, the helicopter falling on grass versus pavement might be less damage extensive because now it's sheer impact damage versus self-inflicted inertia damage.
In short, it depends on *how* you crash

.
I've had a tail servo failure on a mid size electric relatively close to the ground (over grass), but once the blades hit the dirt, the model literally tore it's self to pieces.