Correct.
By playing with the location of the center of mass or CG, we modify the distance that separates that center form the center of lift and drag.

During flight, the plane rotates in any of the three axes only around the CG.

The bigger that separation (CG more forward):
1) There is more lever for the aerodynamic forces to keep or restore the alignment of the center line of the plane with the direction or trajectory of the CG.
2) There is more load on the horizontal tail (and also on the wing), either during upside up or inverted flight. Hence, more elevator surface or deflection is needed for flaring.
3) During loops, the force on the CG increases much as the G's, multiplying the demand on the tail and elevator. Loops of tight radius at high speed are not achievable.

The smaller that separation (CG more aft):
1) There is less lever for the aerodynamic forces to keep or restore the alignment of the center line of the plane with the direction or trajectory of the CG.
2) There is less load on the elevator (and also on the wing), either during upside up or inverted flight. Hence, less elevator surface or deflection is needed for flaring and authority of the elevator during flight is higher (to the point of becoming excessive when the CG is too close to the CL).
3) During loops, the force on the CG imposes less demand on the tail and elevator. Loops of tight radius at high speed are possible.

The airfoil type has nothing to do with those things.
One type lifts more than another for the same variation of AOA, that is all.