Whatever you do take it off first before painting. Assuming it’s a springy stainless steel whip finding a glow in the dark paint that will adhere to that non-reactive surface through rain, hot sun, snow, ice etc might be a challenge. Glow in the dark shrink tubing might be a better and less messy solution.
no, painting it won’t hurt anything, so long as it’s not (as already mentioned) metallic paint. the 2 or 3 antennas in that module already have a layer of plastic over them.