It's hard to say how bad a diaelectric will affect an antenna's tune in the nearfield (~2 wavelengths, but far more critical within 1), and for 5.8G, wavelength is ~2" (52mm). The OEM won't really be able to help (unless they've got a favorite brand to recommend), since the electrical properties of paints can vary WILDLY.
Metalic or conductive paint has a high chance of reflecting the wave back into the antenna (the effect is much more convoluted than this, but gives the basic idea), but "shiny metal looking" doesn't mean it can hold/reflect an EM field.
Plastic paints that close might generate dielectric effects too, but that close to a molded housing, it's probably not going to change much.
It should still work without the housing, but if it was built right, it was tuned with the housing on, so try and preserve it, if you can. This is why I recommend tape-then-paint to see if your chosen paint is going to wreck the performance *before* it becomes perminant.
Found this comment on the web. Might be worth a try.
When I want to test a paint for an antenna, I spray it on an inert object like a paper plate and then pop it into the microwave oven. If the paint stays cool it is RF transparent. If it heats up, don't use it.
But I would add one other possible alternative. Dye. A surprising number of plastics can be dyed with fabric dye which may have less of a dielectric effect. I'm not sure what type of plastic they used so I'm not sure if it would even work...but a pack of black RIT dye is pretty cheap. Just get it good and hot and dunk the plastic for a few minutes and see if it takes.
I do have a set of those antennas (they look like the "neweer" ones sold on ebay - I got mine from emilyandlily on ebay) and the plastic housing isn't that hard to remove. I removed mine fairly easily by doing a flip a bit close to the ground and bouncing it off a bush (flew it out but had to go back to retrieve the cap for my antenna!)
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.