Depends on how sun-fried the tip is. It's certainly not a good thing, but comptips are pretty tough, so it's likely that it's ok.
I had one that was a little fried from being stored mast up with no cover. I shot it with flat black spray paint (I forget the type, I think it was grill paint). In any case, it seemed to work fine and the comptip still looks good a year later. If it's really damaged and has a lot of fibers exposed, you may want to give it a quick sand with 100 or 150 grit paper to knock off the fibers before you shoot it with paint.