In trimmed upside down flight, the rotor would behave exactly as it now does. At trimmed speed, an acceleration would require forward stick, and the rotor would back-flap in a stable manner. The fuselage would apply a resisting moment from the horizontal tail, as well.
I think the belief that the CG effects of the body's mass are dominent is not accurate, and overplays the effects of cg on the basic stability of the aircraft. In most helicopters in normal flight, the CG can be a positive or negative stability term, depending on the relationship to the mast. At aft cg in normal rightside-up flight, the mass is also an unstable term (an increase in G would cause an increase in nose up moment from the cg). This is a real effect, has the same magnitude whether upside down or not, and is easily accounted for in the basic design of the aircraft. In upside down flight, the aft cg would still be de-stabilizing, and a forward cg would be stabilizing.