I install wireless equipment professionally: in-building WiFi and microwave point-to-point links mostly. It's common to paint the radome of outdoor radios to match the buildings they're on. Granted, I have never put the antenna in an anechoic chamber, but there is no noticeable effect that I have ever seen, as long as the paint isn't metallic. I would be really interested to see any range test results. In order to keep the results from being permanent, I would suggest the following protocol:
1. Test range with un-modified antenna.
2. Test range with antenna with masking tape on it.
3. Paint over masking tape, and test range again.
That way the results can be undone if needed, and the effect of the tape itself is controlled for. If additional rigor is desired, the antenna could be swapped on the transmitter, and an observer who didn't know what antenna was being used or what the current distance was could watch to see when the signal broke up. As an additional control, a standard dipole could be used, to help validate the observer: if the observer shows the dipole to have similar or more range than the CP, the experiment is invalidated.
Another approach might be to use a bluescreen display on purpose, since that will provide a consistent, objective measure of when signal has dropped to a certain level. Or, if one had an OSD with RSSI display, a blind observer wouldn't even be needed. One could just measure RSSI at a fixed distance.
It is worth pointing out that, due to the inverse square law, small effects on antenna pattern are magnified over distance, so one should ideally be at a relatively weak RSSI when one performs the testing.
If the radome is removable, another interesting test would be to test the range with the radome off.