Yep, done it many times. Take a look at my Fading & Recoloring Globes album. Works best in direct sunlight, summer prefered. I place them on my deck & leave them for 2-3 weeks. Sometimes, depending on color, it only takes a few days.
If your trying to fade a red/clear that's leaked red into the fluid you may or may not be successful. I've tried to fade the same globe and it never really cleared up, it did a tad but it went back after running it. But other globes I've faded completely using the sun no problem. Globes like the red, black that will leaked wax dye into the fluid, are the ones that will give you issues.
I've seen them under a blacklight and they usually look worse. But you bring up a interesting point. I used to have a red/black 52 oz. next to my UV grande and it always seemed to lose the red in the fluid. I just thought it was cheap dye, but come to think of it the UV bulb may have been the problem.