I'm not an expert, but, after a few minutes with the equations of state, I recall that we find
work produced by a fan or a pump is change in head (corresponds to your change in "static pressure?"

times mass flow rate...
in other words, for fans, it's the product of cfm and delta p times some correction factor to get your favorite units.
The fan curve, then, describes a family of conditions where the fan's work out should factor to a narrow range of work output. We expect various losses would increase with cfm, so the gross power required from the motor would go up (disproportionately) with cfm as well.
For a shut suction, the only work is that of heating up the air, scroll, bearings, etc as the air spins around with the fan instead of flowing. The fan develops the shutoff head (max) at zero flow (min); this defines one end of the fan curve.
As to motor sound, don't we only hear armature speed? I think it can make almost as much noise free-wheeling as at full load. Without some duct hum, would we have much of any way to know what it's doing?
A motor is not like an engine where the higher cylinder pressures tell you of the load even when the tach doesn't change (for example, an engine gets louder starting up a hill, even a stick shift with cruise control.....because it's more work at the same speed).
Don