Yes, the heating process necessary to make the wheel pliable enough to straighten will cause the paint coating on the wheel to fail.
In the rare occurrence where the wheel straightening is required on the front face of the wheel, this will mean you will likely want to have a wheel refurbishment/respray once the wheel has been straightened.
However, if the buckle or flat spot needing straightening is on the inside edge of the wheel, which is far more common, we will spray the wheel to seal it once the straightening is complete. As it is on the inside edge, this will be almost unnoticeable unless looking for it, so most customers do not then opt to pay for a refurbishment afterwards.