Sharpe does NOT work. i had a very talented artist friend do an awesome sharpe design... and it smeared and faded within a few hours. i was only led to believe it would work from another PVC whistle manufacture that recommended it.
The Sharpie will work on many types of PVC and some CPVC. One of the characteristics of many PVC formulations is that it actually absorbs the marker ink into the surface of the plastic. How well it does that may depend on the particular color and the amount of thinner/evaporative in the ink of that pen at the time. But some PVC pipe has a hard surface coating for UV protection, furniture grade pipe for instance, to which the ink won't stick well.
I've been collecting autographs signed with a Sharpie from whistle/flute players on the tubes of my homemade CPVC whistles for ten years or so. They've held up quite well. Of course I don't not play those whistles or subject them to the usual environmental treats my players are subjected to.