Yes the CL will change but the cl curve (is really a straight line) threw most of the non stall angles.
The big difference is the with a non symmetric wing the curve shifts. So that at 0 AOA you have a positive CL instead of 0 with a symmetric foil. And at -1 or -2 deg aoa you will have 0 lift.
so if the plane is flying with 5 Degrees AOA for instance if the prop is adding 2 and subtracting 2, (3 and 7 degrees net) the cl would change the same amount but just in different directions.
HiTech