I don't understand your statement
since the lifting surface is rotating around the aircraft - not sure where you are going with that.
In general, the principles are the same as for fixed wing. If the CofG limits are exceeded, it is possible to run out of control authority to the extent that the aircraft becomes uncontrollable.
Many helicopters, I believe any with a tail rotor, have different left/right CofG limits. The tail rotor opposes the rotation of the fuselage due to torque from the rotor. Since it does this by producing thrust to the side, there is a "translating tendency" which would cause the helicopter to drift in the direction in which the TR is generating lift.
To counter this, the cyclic neutral position is rigged to the left (CCW rotor) or right (CW rotor) which results in the skid on that side hanging low. Clearly, there is now less possible movement in the cyclic to that side and therefore, a narrower lateral CofG.
For example, in a helicopter with a counter-clockwise rotating rotor, the fuselage wants to rotate clockwise. The tail rotor will produce a thrust to the left to counter this and a long lever couple is formed with the main rotor which, if not corrected, would cause the helicopter to drift to the right.
With a perfectly balanced helicopter, in a no wind steady hover, you want the cyclic to be in the centre with no force required from the pilot. To stop the drift to the right, the cyclic is moved to the left. To prevent the need for the pilot to do this, the cyclic is rigged so that its neutral position is to the left. The main rotor thrust vector is now titled to the left which introduces a horizontal component of thrust acting to the left. This also causes the left skid to hang low. This is why in most CCW rotor helicopters, the captain sits on the right and in some of these helicopters, solo flight from the left is prohibited.
Since the cyclic is already left of centre, there is less cyclic authority to the left than to the right. Therefore, the right limit of lateral CofG is less than the left limit.
This could not be achieved by moving the CofG since this would level the fuselage but would not oppose the thrust.
I will never forget the sensation of my first solo lift into the hover after the talking ballast (my instructor) got out and left me to it. I lifted with the control positions where I was used to them. Because there was 170lbs less weight in the front left corner, this meant that I started to pitch up and move back. I was surprised by how much forward and left I had to move the cyclic to counter it. It felt very odd for a few minutes.