UV alone will not kill all parasites, and won't do anything for parasites that are on a fish.
The way UV works is that the tank water is circulated through the chamber, which exposes it to the UV light. Water that passes through the UV chamber will then come back into the tank "clean" of all those little nasties.
How effective a UV unit is depends greatly on the amount of circulation in the tank. Parasites will tend to live in sand beds, on rock, and on the fish. Unless they are in the water that passes through the UV, they would be completely unaffected.