Plants can't use UV spectrum light for normal photosynthetic activity.
So the quick answer is no, you cannot grow plants successfully under JUST black (UV) lights.
The question is, assuming you're growing under conventional lights, will supplementing UV lights add anything?
Some people think THC is a sort of natural sunscreen and that cannabis plants will ramp up THC production under exposure to UV light, so there might be something to this.
Personally, I don't know if this does or doesn't work, but I'm highly skeptical and my bet is on "not". If you could create a meaningful increase in quality just by running black lights, everyone would know this already, and it would be common practice.