Growing with Black Light
Black light lamps—sometimes referred to as Wood's lamps—differ from other light-emitting lamps in that they are designed to produce only electromagnetic radiation in the near-ultraviolet range and very little (or no) visible light. Their effectiveness in growing plants will vary depending on the type of black light lamp used and the plant's reliance on the visible light spectrum, but it is safe to say that a black light would not be ideal for any plant. Plants grown under a black light will tend to grow poorly or fail to grow.
Black Light vs. Grow Light
Grow lights—lamps specifically designed to promote plant growth—are made to produce a range of light similar to that of the sun. This includes many different colors of light. Grow lights tend to produce a bright, almost bluish, white light. Growing plants will not necessarily use all of the light spectrum at once. For example, young growing plants tend to require more in the blue spectrum of light, while older flowering plants require more in the orange and red. For this reason, some plants might germinate and grow under a dark light but will not grow healthy and will likely fail to flower.
Black Light Is not Enough
Almost all plants require the full visible spectrum to flourish. This visible light is excluded by black light lamp manufacturers. Black light lamps would, at best, make an ineffective light source for any plant.